Introduction to Models and Decompositions in Operator Theory

AvCarlos S. Kubrusly

Inbunden, Engelska, 1997

538 kr

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Häftad

538 kr

Beskrivning

Decompositions and models for Hilbert-space operators have been active research topics in recent years, and this book is intended as an introduction to this area of operator theory, working from an abstract point of view. The approach is elementary in that all the proofs only use standard results of single operator thoery, although many of the questions posed in the text lead on to open problems.

Produktinformation

Utgivningsdatum:1997-08-19
Mått:155 x 235 x 13 mm
Vikt:395 g
Format:Inbunden
Språk:Engelska
Antal sidor:132
Upplaga:1997
Förlag:Birkhauser Boston
ISBN:9780817639921

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Beräkning och matematisk analys inom Naturvetenskap och teknik

Innehållsförteckning

0. Preliminaries.- 0.1. Hilbert-Space Operators.- 0.2. Spectrum of an Operator.- 0.3. Convergence and Stability.- 0.4. Projections and Isometries.- 0.5. Invariant Subspaces.- 0.6. Spectral Theorem.- 1. Equivalence.- 1.1. Parts.- 1.2. Norms.- 2. Shifts.- 2.1. Unilateral Shifts.- 2.2. Bilateral Shifts.- 3. Contractions.- 3.1. The Strong Limits of {T*nTn} and {TnT*n}.- 3.2. The Isometry V on R(A)-.- 4. Quasisimilarity.- 4.1. Invariant Subspaces.- 4.2. Hyperinvariant Subspaces.- 4.3. Contractions Quasisimilar to a Unitary Operator.- 5. Decompositions.- 5.1. Nagy-Foia?—Langer Decomposition.- 5.2. von Neumann-Wold Decomposition.- 5.3. A Decomposition for Contractions with A = A2.- 6. Models.- 6.1. Rota’s Model.- 6.2. de Branges-Rovnyak Refinement.- 6.3. Durszt Extension.- 7. Applications.- 7.1. A Pattern for Contractions.- 7.2. Foguel Decomposition.- 8. Similarity.- 8.1. Power Boundedness.- 8.2. Weak and Strong Stability.- References.