Banach Space Complexes:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1995
|
| Schriftenreihe: | Mathematics and Its Applications
334 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The aim of this work is to initiate a systematic study of those properties of Banach space complexes that are stable under certain perturbations. A Banach space complex is essentially an object of the form 1 op-l oP +1 ... --+ XP- --+ XP --+ XP --+ ... , where p runs a finite or infiniteinterval ofintegers, XP are Banach spaces, and oP : Xp ..... Xp+1 are continuous linear operators such that OPOp-1 = 0 for all indices p. In particular, every continuous linear operator S : X ..... Y, where X, Yare Banach spaces, may be regarded as a complex: O ..... X ~ Y ..... O. The already existing Fredholm theory for linear operators suggested the possibility to extend its concepts and methods to the study of Banach space complexes. The basic stability properties valid for (semi-) Fredholm operators have their counterparts in the more general context of Banach space complexes. We have in mind especially the stability of the index (i.e., the extended Euler characteristic) under small or compact perturbations, but other related stability results can also be successfully extended. Banach (or Hilbert) space complexes have penetrated the functional analysis from at least two apparently disjoint directions. A first direction is related to the multivariable spectral theory in the sense of J. L. |
| Beschreibung: | 1 Online-Ressource (V, 213 p) |
| ISBN: | 9789401103756 9789401041683 |
| DOI: | 10.1007/978-94-011-0375-6 |
Internformat
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| 500 | |a The aim of this work is to initiate a systematic study of those properties of Banach space complexes that are stable under certain perturbations. A Banach space complex is essentially an object of the form 1 op-l oP +1 ... --+ XP- --+ XP --+ XP --+ ... , where p runs a finite or infiniteinterval ofintegers, XP are Banach spaces, and oP : Xp ..... Xp+1 are continuous linear operators such that OPOp-1 = 0 for all indices p. In particular, every continuous linear operator S : X ..... Y, where X, Yare Banach spaces, may be regarded as a complex: O ..... X ~ Y ..... O. The already existing Fredholm theory for linear operators suggested the possibility to extend its concepts and methods to the study of Banach space complexes. The basic stability properties valid for (semi-) Fredholm operators have their counterparts in the more general context of Banach space complexes. We have in mind especially the stability of the index (i.e., the extended Euler characteristic) under small or compact perturbations, but other related stability results can also be successfully extended. Banach (or Hilbert) space complexes have penetrated the functional analysis from at least two apparently disjoint directions. A first direction is related to the multivariable spectral theory in the sense of J. L. | ||
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| 650 | 4 | |a Partial Differential Equations | |
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Datensatz im Suchindex
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| classification_tum | MAT 000 |
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| ctrlnum | (OCoLC)1184431118 (DE-599)BVBBV042423818 |
| dewey-full | 515.724 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.724 |
| dewey-search | 515.724 |
| dewey-sort | 3515.724 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-94-011-0375-6 |
| format | Electronic eBook |
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| institution | BVB |
| isbn | 9789401103756 9789401041683 |
| language | English |
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| spelling | Ambrozie, Cǎlin-Grigore Verfasser aut Banach Space Complexes edited by Cǎlin-Grigore Ambrozie, Florian-Horia Vasilescu Dordrecht Springer Netherlands 1995 1 Online-Ressource (V, 213 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 334 The aim of this work is to initiate a systematic study of those properties of Banach space complexes that are stable under certain perturbations. A Banach space complex is essentially an object of the form 1 op-l oP +1 ... --+ XP- --+ XP --+ XP --+ ... , where p runs a finite or infiniteinterval ofintegers, XP are Banach spaces, and oP : Xp ..... Xp+1 are continuous linear operators such that OPOp-1 = 0 for all indices p. In particular, every continuous linear operator S : X ..... Y, where X, Yare Banach spaces, may be regarded as a complex: O ..... X ~ Y ..... O. The already existing Fredholm theory for linear operators suggested the possibility to extend its concepts and methods to the study of Banach space complexes. The basic stability properties valid for (semi-) Fredholm operators have their counterparts in the more general context of Banach space complexes. We have in mind especially the stability of the index (i.e., the extended Euler characteristic) under small or compact perturbations, but other related stability results can also be successfully extended. Banach (or Hilbert) space complexes have penetrated the functional analysis from at least two apparently disjoint directions. A first direction is related to the multivariable spectral theory in the sense of J. L. Mathematics Functional analysis Integral Transforms Operator theory Differential equations, partial Operator Theory Functional Analysis Integral Transforms, Operational Calculus Partial Differential Equations Several Complex Variables and Analytic Spaces Mathematik Komplex Topologie (DE-588)4164883-3 gnd rswk-swf Banach-Raum (DE-588)4004402-6 gnd rswk-swf Banach-Raum (DE-588)4004402-6 s Komplex Topologie (DE-588)4164883-3 s 1\p DE-604 Vasilescu, Florian-Horia Sonstige oth https://doi.org/10.1007/978-94-011-0375-6 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Ambrozie, Cǎlin-Grigore Banach Space Complexes Mathematics Functional analysis Integral Transforms Operator theory Differential equations, partial Operator Theory Functional Analysis Integral Transforms, Operational Calculus Partial Differential Equations Several Complex Variables and Analytic Spaces Mathematik Komplex Topologie (DE-588)4164883-3 gnd Banach-Raum (DE-588)4004402-6 gnd |
| subject_GND | (DE-588)4164883-3 (DE-588)4004402-6 |
| title | Banach Space Complexes |
| title_auth | Banach Space Complexes |
| title_exact_search | Banach Space Complexes |
| title_full | Banach Space Complexes edited by Cǎlin-Grigore Ambrozie, Florian-Horia Vasilescu |
| title_fullStr | Banach Space Complexes edited by Cǎlin-Grigore Ambrozie, Florian-Horia Vasilescu |
| title_full_unstemmed | Banach Space Complexes edited by Cǎlin-Grigore Ambrozie, Florian-Horia Vasilescu |
| title_short | Banach Space Complexes |
| title_sort | banach space complexes |
| topic | Mathematics Functional analysis Integral Transforms Operator theory Differential equations, partial Operator Theory Functional Analysis Integral Transforms, Operational Calculus Partial Differential Equations Several Complex Variables and Analytic Spaces Mathematik Komplex Topologie (DE-588)4164883-3 gnd Banach-Raum (DE-588)4004402-6 gnd |
| topic_facet | Mathematics Functional analysis Integral Transforms Operator theory Differential equations, partial Operator Theory Functional Analysis Integral Transforms, Operational Calculus Partial Differential Equations Several Complex Variables and Analytic Spaces Mathematik Komplex Topologie Banach-Raum |
| url | https://doi.org/10.1007/978-94-011-0375-6 |
| work_keys_str_mv | AT ambroziecalingrigore banachspacecomplexes AT vasilescuflorianhoria banachspacecomplexes |