Banach Space Complexes by C.-G. AmbrozieBanach Space Complexes by C.-G. Ambrozie

Banach Space Complexes

byC.-G. Ambrozie, Florian-Horia Vasilescu

Paperback | November 22, 2012

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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 <_20_y20_.....20_o.20_the20_already20_existing20_fredholm20_theory20_for20_linear20_operators20_suggested20_the20_possibility20_to20_extend20_its20_concepts20_and20_methods20_to20_the20_study20_of20_banach20_space20_complexes.20_the20_basic20_stability20_properties20_valid20_for20_28_semi-29_20_fredholm20_operators20_have20_their20_counterparts20_in20_the20_more20_general20_context20_of20_banach20_space20_complexes.20_we20_have20_in20_mind20_especially20_the20_stability20_of20_the20_index20_28_i.e.2c_20_the20_extended20_euler20_characteristic29_20_under20_small20_or20_compact20_perturbations2c_20_but20_other20_related20_stability20_results20_can20_also20_be20_successfully20_extended.20_banach20_28_or20_hilbert29_20_space20_complexes20_have20_penetrated20_the20_functional20_analysis20_from20_at20_least20_two20_apparently20_disjoint20_directions.20_a20_first20_direction20_is20_related20_to20_the20_multivariable20_spectral20_theory20_in20_the20_sense20_of20_j.20_l. y="" .....="" o.="" the="" already="" existing="" fredholm="" theory="" for="" linear="" operators="" suggested="" possibility="" to="" extend="" its="" concepts="" and="" methods="" study="" of="" banach="" space="" complexes.="" basic="" stability="" properties="" valid="" _28_semi-29_="" have="" their="" counterparts="" in="" more="" general="" context="" we="" mind="" especially="" index="" _28_i.e.2c_="" extended="" euler="" _characteristic29_="" under="" small="" or="" compact="" _perturbations2c_="" but="" other="" related="" results="" can="" also="" be="" successfully="" extended.="" _28_or="" _hilbert29_="" complexes="" penetrated="" functional="" analysis="" from="" at="" least="" two="" apparently="" disjoint="" directions.="" a="" first="" direction="" is="" multivariable="" spectral="" sense="" j.="">
Title:Banach Space ComplexesFormat:PaperbackDimensions:213 pagesPublished:November 22, 2012Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9401041687

ISBN - 13:9789401041683

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Table of Contents

Introduction. I: Preliminaries. 1. Algebraic prerequisites. 2. Algebraic Fredholm pairs. 3. Paraclosed linear transformations. 4. Homogeneous operators. 5. Linear and homogeneous projections and liftings. 6. The gap between two closed subspaces. 7. Linear operators with closed range, and finite extensions. 8. Metric relations and duality. 9. Operators in quotient Banach spaces. 10. References and comments. II: Semi-Fredholm complexes. 1. Semi-Fredholm operators. 2. Semi-Fredholm complexes. 3. Essential complexes. 4. Fredholm pairs. 5. Other continuous invariants. 6. References and comments. III: Related topics. 1. Joint spectra and perturbations. 2. Spectral interpolation and perturbations. 3. Versions of Poincaré's and Grothendieck's lemmas. 4. Differentiable families of partial differential operators. 5. References and comments. Subject index. Notations. Bibliography.