Fredholmness of a linear combination of operators
Although it is well known that Fredholmness of the linear combination α P + β Q , α , β ∈ C ∖ { 0 } , α + β ≠ 0 , does not depend on the choice of scalars if P , Q ∈ B ( H ) are idempotents, no necessary and sufficient conditions for Fredholmness of this linear combination are yet known, except for...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Cvetković-Ilić, D. [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2018transfer abstract |
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| Schlagwörter: |
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| Umfang: |
11 |
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| Übergeordnetes Werk: |
Enthalten in: In silico drug repurposing in COVID-19: A network-based analysis - Sibilio, Pasquale ELSEVIER, 2021, Amsterdam [u.a.] |
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| Übergeordnetes Werk: |
volume:458 ; year:2018 ; number:1 ; day:1 ; month:02 ; pages:555-565 ; extent:11 |
| Links: |
|---|
| DOI / URN: |
10.1016/j.jmaa.2017.09.027 |
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ELV040618943 |
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| 520 | |a Although it is well known that Fredholmness of the linear combination α P + β Q , α , β ∈ C ∖ { 0 } , α + β ≠ 0 , does not depend on the choice of scalars if P , Q ∈ B ( H ) are idempotents, no necessary and sufficient conditions for Fredholmness of this linear combination are yet known, except for the special case when P and Q are orthogonal projectors. In this paper, using a completely different approach and some results on completion problems of operator matrices, we give necessary and sufficient conditions for Fredholmness of a sum of two idempotents. Also, we will discuss the more general question when the sum of two operators is a Fredholm operator and consider some special cases when Fredholmness of a linear combination of two operators is independent of the choice of the scalars. On the other hand some special classes of operators for which a linear combination of two operators depends of the choice of the scalars are listed. A new proof of a well-known result is given. | ||
| 520 | |a Although it is well known that Fredholmness of the linear combination α P + β Q , α , β ∈ C ∖ { 0 } , α + β ≠ 0 , does not depend on the choice of scalars if P , Q ∈ B ( H ) are idempotents, no necessary and sufficient conditions for Fredholmness of this linear combination are yet known, except for the special case when P and Q are orthogonal projectors. In this paper, using a completely different approach and some results on completion problems of operator matrices, we give necessary and sufficient conditions for Fredholmness of a sum of two idempotents. Also, we will discuss the more general question when the sum of two operators is a Fredholm operator and consider some special cases when Fredholmness of a linear combination of two operators is independent of the choice of the scalars. On the other hand some special classes of operators for which a linear combination of two operators depends of the choice of the scalars are listed. A new proof of a well-known result is given. | ||
| 650 | 7 | |a Orthogonal projection |2 Elsevier | |
| 650 | 7 | |a Operator matrices |2 Elsevier | |
| 650 | 7 | |a Idempotent |2 Elsevier | |
| 650 | 7 | |a Completions problems |2 Elsevier | |
| 650 | 7 | |a Fredholm operators |2 Elsevier | |
| 700 | 1 | |a Milošević, J. |4 oth | |
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10.1016/j.jmaa.2017.09.027 doi GBV00000000000318_01.pica (DE-627)ELV040618943 (ELSEVIER)S0022-247X(17)30856-9 DE-627 ger DE-627 rakwb eng 610 VZ 44.40 bkl Cvetković-Ilić, D. verfasserin aut Fredholmness of a linear combination of operators 2018transfer abstract 11 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Although it is well known that Fredholmness of the linear combination α P + β Q , α , β ∈ C ∖ { 0 } , α + β ≠ 0 , does not depend on the choice of scalars if P , Q ∈ B ( H ) are idempotents, no necessary and sufficient conditions for Fredholmness of this linear combination are yet known, except for the special case when P and Q are orthogonal projectors. In this paper, using a completely different approach and some results on completion problems of operator matrices, we give necessary and sufficient conditions for Fredholmness of a sum of two idempotents. Also, we will discuss the more general question when the sum of two operators is a Fredholm operator and consider some special cases when Fredholmness of a linear combination of two operators is independent of the choice of the scalars. On the other hand some special classes of operators for which a linear combination of two operators depends of the choice of the scalars are listed. A new proof of a well-known result is given. Although it is well known that Fredholmness of the linear combination α P + β Q , α , β ∈ C ∖ { 0 } , α + β ≠ 0 , does not depend on the choice of scalars if P , Q ∈ B ( H ) are idempotents, no necessary and sufficient conditions for Fredholmness of this linear combination are yet known, except for the special case when P and Q are orthogonal projectors. In this paper, using a completely different approach and some results on completion problems of operator matrices, we give necessary and sufficient conditions for Fredholmness of a sum of two idempotents. Also, we will discuss the more general question when the sum of two operators is a Fredholm operator and consider some special cases when Fredholmness of a linear combination of two operators is independent of the choice of the scalars. On the other hand some special classes of operators for which a linear combination of two operators depends of the choice of the scalars are listed. A new proof of a well-known result is given. Orthogonal projection Elsevier Operator matrices Elsevier Idempotent Elsevier Completions problems Elsevier Fredholm operators Elsevier Milošević, J. oth Enthalten in Elsevier Sibilio, Pasquale ELSEVIER In silico drug repurposing in COVID-19: A network-based analysis 2021 Amsterdam [u.a.] (DE-627)ELV006634001 volume:458 year:2018 number:1 day:1 month:02 pages:555-565 extent:11 https://doi.org/10.1016/j.jmaa.2017.09.027 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA SSG-OPC-PHA 44.40 Pharmazie Pharmazeutika VZ AR 458 2018 1 1 0201 555-565 11 |
| spelling |
10.1016/j.jmaa.2017.09.027 doi GBV00000000000318_01.pica (DE-627)ELV040618943 (ELSEVIER)S0022-247X(17)30856-9 DE-627 ger DE-627 rakwb eng 610 VZ 44.40 bkl Cvetković-Ilić, D. verfasserin aut Fredholmness of a linear combination of operators 2018transfer abstract 11 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Although it is well known that Fredholmness of the linear combination α P + β Q , α , β ∈ C ∖ { 0 } , α + β ≠ 0 , does not depend on the choice of scalars if P , Q ∈ B ( H ) are idempotents, no necessary and sufficient conditions for Fredholmness of this linear combination are yet known, except for the special case when P and Q are orthogonal projectors. In this paper, using a completely different approach and some results on completion problems of operator matrices, we give necessary and sufficient conditions for Fredholmness of a sum of two idempotents. Also, we will discuss the more general question when the sum of two operators is a Fredholm operator and consider some special cases when Fredholmness of a linear combination of two operators is independent of the choice of the scalars. On the other hand some special classes of operators for which a linear combination of two operators depends of the choice of the scalars are listed. A new proof of a well-known result is given. Although it is well known that Fredholmness of the linear combination α P + β Q , α , β ∈ C ∖ { 0 } , α + β ≠ 0 , does not depend on the choice of scalars if P , Q ∈ B ( H ) are idempotents, no necessary and sufficient conditions for Fredholmness of this linear combination are yet known, except for the special case when P and Q are orthogonal projectors. In this paper, using a completely different approach and some results on completion problems of operator matrices, we give necessary and sufficient conditions for Fredholmness of a sum of two idempotents. Also, we will discuss the more general question when the sum of two operators is a Fredholm operator and consider some special cases when Fredholmness of a linear combination of two operators is independent of the choice of the scalars. On the other hand some special classes of operators for which a linear combination of two operators depends of the choice of the scalars are listed. A new proof of a well-known result is given. Orthogonal projection Elsevier Operator matrices Elsevier Idempotent Elsevier Completions problems Elsevier Fredholm operators Elsevier Milošević, J. oth Enthalten in Elsevier Sibilio, Pasquale ELSEVIER In silico drug repurposing in COVID-19: A network-based analysis 2021 Amsterdam [u.a.] (DE-627)ELV006634001 volume:458 year:2018 number:1 day:1 month:02 pages:555-565 extent:11 https://doi.org/10.1016/j.jmaa.2017.09.027 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA SSG-OPC-PHA 44.40 Pharmazie Pharmazeutika VZ AR 458 2018 1 1 0201 555-565 11 |
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10.1016/j.jmaa.2017.09.027 doi GBV00000000000318_01.pica (DE-627)ELV040618943 (ELSEVIER)S0022-247X(17)30856-9 DE-627 ger DE-627 rakwb eng 610 VZ 44.40 bkl Cvetković-Ilić, D. verfasserin aut Fredholmness of a linear combination of operators 2018transfer abstract 11 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Although it is well known that Fredholmness of the linear combination α P + β Q , α , β ∈ C ∖ { 0 } , α + β ≠ 0 , does not depend on the choice of scalars if P , Q ∈ B ( H ) are idempotents, no necessary and sufficient conditions for Fredholmness of this linear combination are yet known, except for the special case when P and Q are orthogonal projectors. In this paper, using a completely different approach and some results on completion problems of operator matrices, we give necessary and sufficient conditions for Fredholmness of a sum of two idempotents. Also, we will discuss the more general question when the sum of two operators is a Fredholm operator and consider some special cases when Fredholmness of a linear combination of two operators is independent of the choice of the scalars. On the other hand some special classes of operators for which a linear combination of two operators depends of the choice of the scalars are listed. A new proof of a well-known result is given. Although it is well known that Fredholmness of the linear combination α P + β Q , α , β ∈ C ∖ { 0 } , α + β ≠ 0 , does not depend on the choice of scalars if P , Q ∈ B ( H ) are idempotents, no necessary and sufficient conditions for Fredholmness of this linear combination are yet known, except for the special case when P and Q are orthogonal projectors. In this paper, using a completely different approach and some results on completion problems of operator matrices, we give necessary and sufficient conditions for Fredholmness of a sum of two idempotents. Also, we will discuss the more general question when the sum of two operators is a Fredholm operator and consider some special cases when Fredholmness of a linear combination of two operators is independent of the choice of the scalars. On the other hand some special classes of operators for which a linear combination of two operators depends of the choice of the scalars are listed. A new proof of a well-known result is given. Orthogonal projection Elsevier Operator matrices Elsevier Idempotent Elsevier Completions problems Elsevier Fredholm operators Elsevier Milošević, J. oth Enthalten in Elsevier Sibilio, Pasquale ELSEVIER In silico drug repurposing in COVID-19: A network-based analysis 2021 Amsterdam [u.a.] (DE-627)ELV006634001 volume:458 year:2018 number:1 day:1 month:02 pages:555-565 extent:11 https://doi.org/10.1016/j.jmaa.2017.09.027 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA SSG-OPC-PHA 44.40 Pharmazie Pharmazeutika VZ AR 458 2018 1 1 0201 555-565 11 |
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10.1016/j.jmaa.2017.09.027 doi GBV00000000000318_01.pica (DE-627)ELV040618943 (ELSEVIER)S0022-247X(17)30856-9 DE-627 ger DE-627 rakwb eng 610 VZ 44.40 bkl Cvetković-Ilić, D. verfasserin aut Fredholmness of a linear combination of operators 2018transfer abstract 11 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Although it is well known that Fredholmness of the linear combination α P + β Q , α , β ∈ C ∖ { 0 } , α + β ≠ 0 , does not depend on the choice of scalars if P , Q ∈ B ( H ) are idempotents, no necessary and sufficient conditions for Fredholmness of this linear combination are yet known, except for the special case when P and Q are orthogonal projectors. In this paper, using a completely different approach and some results on completion problems of operator matrices, we give necessary and sufficient conditions for Fredholmness of a sum of two idempotents. Also, we will discuss the more general question when the sum of two operators is a Fredholm operator and consider some special cases when Fredholmness of a linear combination of two operators is independent of the choice of the scalars. On the other hand some special classes of operators for which a linear combination of two operators depends of the choice of the scalars are listed. A new proof of a well-known result is given. Although it is well known that Fredholmness of the linear combination α P + β Q , α , β ∈ C ∖ { 0 } , α + β ≠ 0 , does not depend on the choice of scalars if P , Q ∈ B ( H ) are idempotents, no necessary and sufficient conditions for Fredholmness of this linear combination are yet known, except for the special case when P and Q are orthogonal projectors. In this paper, using a completely different approach and some results on completion problems of operator matrices, we give necessary and sufficient conditions for Fredholmness of a sum of two idempotents. Also, we will discuss the more general question when the sum of two operators is a Fredholm operator and consider some special cases when Fredholmness of a linear combination of two operators is independent of the choice of the scalars. On the other hand some special classes of operators for which a linear combination of two operators depends of the choice of the scalars are listed. A new proof of a well-known result is given. Orthogonal projection Elsevier Operator matrices Elsevier Idempotent Elsevier Completions problems Elsevier Fredholm operators Elsevier Milošević, J. oth Enthalten in Elsevier Sibilio, Pasquale ELSEVIER In silico drug repurposing in COVID-19: A network-based analysis 2021 Amsterdam [u.a.] (DE-627)ELV006634001 volume:458 year:2018 number:1 day:1 month:02 pages:555-565 extent:11 https://doi.org/10.1016/j.jmaa.2017.09.027 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA SSG-OPC-PHA 44.40 Pharmazie Pharmazeutika VZ AR 458 2018 1 1 0201 555-565 11 |
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10.1016/j.jmaa.2017.09.027 doi GBV00000000000318_01.pica (DE-627)ELV040618943 (ELSEVIER)S0022-247X(17)30856-9 DE-627 ger DE-627 rakwb eng 610 VZ 44.40 bkl Cvetković-Ilić, D. verfasserin aut Fredholmness of a linear combination of operators 2018transfer abstract 11 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Although it is well known that Fredholmness of the linear combination α P + β Q , α , β ∈ C ∖ { 0 } , α + β ≠ 0 , does not depend on the choice of scalars if P , Q ∈ B ( H ) are idempotents, no necessary and sufficient conditions for Fredholmness of this linear combination are yet known, except for the special case when P and Q are orthogonal projectors. In this paper, using a completely different approach and some results on completion problems of operator matrices, we give necessary and sufficient conditions for Fredholmness of a sum of two idempotents. Also, we will discuss the more general question when the sum of two operators is a Fredholm operator and consider some special cases when Fredholmness of a linear combination of two operators is independent of the choice of the scalars. On the other hand some special classes of operators for which a linear combination of two operators depends of the choice of the scalars are listed. A new proof of a well-known result is given. Although it is well known that Fredholmness of the linear combination α P + β Q , α , β ∈ C ∖ { 0 } , α + β ≠ 0 , does not depend on the choice of scalars if P , Q ∈ B ( H ) are idempotents, no necessary and sufficient conditions for Fredholmness of this linear combination are yet known, except for the special case when P and Q are orthogonal projectors. In this paper, using a completely different approach and some results on completion problems of operator matrices, we give necessary and sufficient conditions for Fredholmness of a sum of two idempotents. Also, we will discuss the more general question when the sum of two operators is a Fredholm operator and consider some special cases when Fredholmness of a linear combination of two operators is independent of the choice of the scalars. On the other hand some special classes of operators for which a linear combination of two operators depends of the choice of the scalars are listed. A new proof of a well-known result is given. Orthogonal projection Elsevier Operator matrices Elsevier Idempotent Elsevier Completions problems Elsevier Fredholm operators Elsevier Milošević, J. oth Enthalten in Elsevier Sibilio, Pasquale ELSEVIER In silico drug repurposing in COVID-19: A network-based analysis 2021 Amsterdam [u.a.] (DE-627)ELV006634001 volume:458 year:2018 number:1 day:1 month:02 pages:555-565 extent:11 https://doi.org/10.1016/j.jmaa.2017.09.027 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U SSG-OLC-PHA SSG-OPC-PHA 44.40 Pharmazie Pharmazeutika VZ AR 458 2018 1 1 0201 555-565 11 |
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English |
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Enthalten in In silico drug repurposing in COVID-19: A network-based analysis Amsterdam [u.a.] volume:458 year:2018 number:1 day:1 month:02 pages:555-565 extent:11 |
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Enthalten in In silico drug repurposing in COVID-19: A network-based analysis Amsterdam [u.a.] volume:458 year:2018 number:1 day:1 month:02 pages:555-565 extent:11 |
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In silico drug repurposing in COVID-19: A network-based analysis |
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In this paper, using a completely different approach and some results on completion problems of operator matrices, we give necessary and sufficient conditions for Fredholmness of a sum of two idempotents. Also, we will discuss the more general question when the sum of two operators is a Fredholm operator and consider some special cases when Fredholmness of a linear combination of two operators is independent of the choice of the scalars. On the other hand some special classes of operators for which a linear combination of two operators depends of the choice of the scalars are listed. 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In silico drug repurposing in COVID-19: A network-based analysis |
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Fredholmness of a linear combination of operators |
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Although it is well known that Fredholmness of the linear combination α P + β Q , α , β ∈ C ∖ { 0 } , α + β ≠ 0 , does not depend on the choice of scalars if P , Q ∈ B ( H ) are idempotents, no necessary and sufficient conditions for Fredholmness of this linear combination are yet known, except for the special case when P and Q are orthogonal projectors. In this paper, using a completely different approach and some results on completion problems of operator matrices, we give necessary and sufficient conditions for Fredholmness of a sum of two idempotents. Also, we will discuss the more general question when the sum of two operators is a Fredholm operator and consider some special cases when Fredholmness of a linear combination of two operators is independent of the choice of the scalars. On the other hand some special classes of operators for which a linear combination of two operators depends of the choice of the scalars are listed. A new proof of a well-known result is given. |
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Although it is well known that Fredholmness of the linear combination α P + β Q , α , β ∈ C ∖ { 0 } , α + β ≠ 0 , does not depend on the choice of scalars if P , Q ∈ B ( H ) are idempotents, no necessary and sufficient conditions for Fredholmness of this linear combination are yet known, except for the special case when P and Q are orthogonal projectors. In this paper, using a completely different approach and some results on completion problems of operator matrices, we give necessary and sufficient conditions for Fredholmness of a sum of two idempotents. Also, we will discuss the more general question when the sum of two operators is a Fredholm operator and consider some special cases when Fredholmness of a linear combination of two operators is independent of the choice of the scalars. On the other hand some special classes of operators for which a linear combination of two operators depends of the choice of the scalars are listed. A new proof of a well-known result is given. |
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Although it is well known that Fredholmness of the linear combination α P + β Q , α , β ∈ C ∖ { 0 } , α + β ≠ 0 , does not depend on the choice of scalars if P , Q ∈ B ( H ) are idempotents, no necessary and sufficient conditions for Fredholmness of this linear combination are yet known, except for the special case when P and Q are orthogonal projectors. In this paper, using a completely different approach and some results on completion problems of operator matrices, we give necessary and sufficient conditions for Fredholmness of a sum of two idempotents. Also, we will discuss the more general question when the sum of two operators is a Fredholm operator and consider some special cases when Fredholmness of a linear combination of two operators is independent of the choice of the scalars. On the other hand some special classes of operators for which a linear combination of two operators depends of the choice of the scalars are listed. A new proof of a well-known result is given. |
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