Classes of Linear Operators Volume 1 and 2
Birkhäuser Verlag GmbH
Published in September 1993
Book
Hardback
566 pages
978-3-7643-2944-0 (ISBN)
Article exhausted; check different version
Description
This - book offers a panoptic view of operator theory. It treats a variety of classes of linear operators which illustrate the richness of the theory, both in its theoretical developments and its applications. For each of the classes various differential and integral operators motivate or illustrate the main results. The topics have been updated and enhanced by new developments, many of which appear here for the first time. Interconnections appear frequently and unexpectedly. This second volume consists of five parts: triangular representations, classes of Toeplitz operators, contractive operators and characteristic operator functions, Banach algebras and algebras of operators, and extension and completion problems. The exposition is self-contained and has been simplified and polished in an effort to make advanced topics accessible to a wide audience of students and researchers in mathematics, science and engineering.
More details
Series
Language
German
Place of publication
Basel
Switzerland
Target group
College/higher education
Professional and scholarly
Dimensions
Height: 240 mm
Weight
1228 gr
ISBN-13
978-3-7643-2944-0 (9783764329440)
Schweitzer Classification
Other editions
Additional editions

Israel Gohberg | Seymour Goldberg | Marius a. Kaashoek
Classes of Linear Operators
Book
11/2012
Birkhäuser
€85.59
Shipment within 10-15 days
Content
Preface to Volume II. Table of contents of Volume II. Introduction. PART V: TRIANGULAR REPRESENTATIONS XX. Additive lower-upper triangular decompositions of operators 1. Additive lower-upper triangular decompositions relative to finite chains 2. Preliminaries about chains 3. Diagonals 4. Chains on Hilbert space 5. Triangular algebras 6. Riemann-Stieltjes integration along chains 7. Additive lower-upper decomposition theorem 8. Additive lower-upper decomposition of a Hilbert-Schmidt operator 9. Multiplicative integration along chains 10. Basic properties of reproducing kernel Hilbert spaces and chains 11. Example of an additive LU-decomposition in a RKHS. XXI. Operators in triangular form 1. Triangular representation 2. Intermezzo about completely nonselfadjoint operators 3. Volterra operators with a one-dimensional imaginary part 4. Unicellular operators. XXII. Multiplicative lower-upper triangular decompositions of operators 1. LU-factorization with respect to a finite chain 2. The LU-factorization theorem 3. LU-factorizations of compact perturbations of the identity 4. LU-factorizatioris of Hilbert-Schmidt perturbations of the identity 5. LU-factorizations of integral operators 6. Triangular representations of operators close to unitary 7. LU-factorization of semi-separable integral operators 8. Generalised Wiener-Hopf equations 9. Generalised LU-factorization relative to discrete chains. Comments on Part V Exercises to Part V PART VI: CLASSES OF TOEPLITZ OPERATORS XXIII. Block Toeplitz operators 1 Preliminaries 2. Block Laurent operators 3. Block Toeplitz operators 4. Block Toeplitz operators defined by continuous functions 5. The Fredholm index of a block Toeplitz operator defined by a continuous function. XXIV. Toeplitz operators defined by rational matrix functions 1. Preliminaries 2. Invertibility and Fredholm index (scalar case) 3. Wiener-Hopf factorization 4. Invertibility and Fredholm index (matrix case) 5. Intermezzo about realisation 6. Inversion of a block Laurent operator 7. Explicit canonical factorization 8. Explicit inversion formulas 9. Explicit formulas for Fredholm characteristics 10. An example 11. Asymptotic formulas for determinants of block Toeplitz matrices. XXV. Toeplitz operators defined by piecewise continuous matrix functions 1. Piecewise continuous functions 2. Symbol and Fredholm index (scalar case) 3. Symbol and Fredholm index (matrix case) 4. Sums of products of Toeplitz operators defined by piecewise continuous functions 5. Sums of products of block Toeplitz operators defined by piecewise continuous functions. Comments on Part VI. Exercises to Part VI. PART VII: CONTRACTIVE OPERATORS AND CHARACTERISTIC OPERATOR FUNCTIONS XXVI. Block shift operators 1. Forward shifts and isometries 2. Parts of block shift operators 3. Invariant subspaces of forward shift operators. XXVII. Dilation theory 1. Preliminaries about contractions 2. Preliminaries about dilations 3. Isometric dilations 4. Unitary dilations