Operator Theory and Complex Analysis: Workshop on Operator Theory and Complex Analysis Sapporo (Japan) June 1991

✍ Scribed by Vadim Adamyan (auth.), Prof. T. Ando, Prof. I. Gohberg (eds.)

• Publisher: Birkhäuser Basel
• Year: 1992
• Tongue: English
• Leaves: 417
• Series: Operator Theory: Advances and Applications 59
• Edition: 1
• Category: Library

✦ Synopsis

Scattering matrices for microschemes.- 1. General expressions for the scattering matrix.- 2. Continuity condition.- References.- Holomorphic operators between Krein spaces and the number of squares of associated kernels.- 0. Introduction.- 1. Realizations of a class of Schur functions.- 2. Positive squares and injectivity.- 3. Application of the Potapov-Ginzburg transform.- References.- On reproducing kernel spaces, the Schur algorithm, and interpolation in a general class of domains.- 1. Introduction.- 2. Preliminaries.- 3. B(X) spaces.- 4. Recursive extractions and the Schur algorithm.- 5. H?(S) spaces.- 6. Linear fractional transformations.- 7. One sided interpolation.- 8. References.- The central method for positive semi-definite, contractive and strong Parrott type completion problems.- 1. Introduction.- 2. Positive semi-definite completions.- 3. Contractive completions.- 4. Linearly constrained contractive completions.- References.- Interpolation by rational matrix functions and stability of feedback systems: The 4-block case.- 1. Preliminaries.- 2. A homogeneous interpolation problem.- 3. Interpolation problem.- 4. Parametrization of solutions.- 5. Interpolation and internally stable feedback systems.- References.- Matricial coupling and equivalence after extension.- 1. Introduction.- 2. Coupling versus equivalence.- 3. Examples.- 4. Special classes of operators.- References.- Operator means and the relative operator entropy.- 1. Introduction.- 2. Origins of operator means.- 3. Operator means and operator monotone functions.- 4. Operator concave functions and Jensen’s inequality.- 5. Relative operator entropy.- References.- An application of Furuta’s inequality to Ando’s theorem.- 1. Introduction.- 2. Operator functions.- 3. Furuta’s type inequalities.- 4. An application to Ando’s theorem.- References.- Applications of order preserving operator inequalities.- 0. Introduction.- 1. Application to the relative operator entropy.- 2. Application to some extended result of Ando’s one.- References.- The band extension of the real line as a limit of discrete band extensions, I. The main limit theorem.- 0. Introduction.- I. Preliminaries and preparations.- II. Band extensions.- III. Continuous versus discrete.- References.- Interpolating sequences in the maximal ideal space of H? II.- 1. Introduction.- 2. Condition (A2).- 3. Condition (A3).- 4. Condition (A1).- References.- Operator matrices with chordal inverse patterns.- 1. Introduction.- 2. Entry formulae.- 3. Inertia formula.- References.- Models and unitary equivalence of cyclic selfadjoint operators in Pontrjagin spaces.- 1. The class F of linear functionals.- 2. The Pontrjagin space associated with ? ? F.- 3. Models for cyclic selfadjoint operators in Pontrjagin spaces.- 4. Unitary equivalence of cyclic selfadjoint operators in Pontrjagin spaces.- References.- The von Neumann inequality and dilation theorems for contractions.- 1. The von Neumann inequality and strong unitary dilation.- 2. Canonical representation of completely contractive maps.- 3. An effect of generation of nuclear algebras.- References.- Interpolation problems, inverse spectral problems and nonlinear equations.- References.- Extended interpolation problem in finitely connected domains.- I. Matrices and transformation formulas.- II. Disc Cases.- III. Domains of finite connectivity.- References.- Accretive extensions and problems on the Stieltjes operator-valued functions relations.- 1. Accretive and sectorial extensions of the positive operators, operators of the class C(?) and their parametric representation.- 2. Stieltjes operator-valued functions and their realization.- 3. M.S. Livsic triangular model of the M-accretive extensions (with real spectrum) of the positive operators.- 4. Canonical and generalized resolvents of QSC-extensions of Hermitian contractions.- References.- Commuting nonselfadjoint operators and algebraic curves.- 1. Commuting nonselfadjoint operators and the discriminant curve.- 2. Determinantal representations of real plane curves.- 3. Commutative operator colligations.- 4. Construction of triangular models: Finite-dimensional case.- 5. Construction of triangular models: General case.- 6. Characteristic functions and the factorization theorem.- References.- All (?) about quasinormal operators.- 1. Introduction.- 2. Representations.- 3. Spectrum and multiplicity.- 4. Special classes.- 5. Invariant subspaces.- 6. Commutant.- 7. Similarity.- 8. Quasisimilarity.- 9. Compact perturbation.- 10. Open problems.- References.- Workshop Program.- List of Participants.

✦ Table of Contents

Front Matter....Pages I-X
Scattering Matrices for Micro Schemes....Pages 1-10
Holomorphic Operators Between Krein Spaces and the Number of Squares of Associated Kernels....Pages 11-29
On Reproducing Kernel Spaces, The Schur Algorithm, and Interpolation in a General Class of Domains....Pages 30-77
The Central Method for Positive Semi-Definite, Contractive and Strong Parrott Type Completion Problems....Pages 78-95
Interpolation by Rational Matrix Functions and Stability of Feedback Systems: The 4-Block Case....Pages 96-142
Matricial Coupling and Equivalence After Extension....Pages 143-160
Operator Means and the Relative Operator Entropy....Pages 161-172
An Application of Furuta’s Inequality to Ando’s Theorem....Pages 173-179
Applications of Order Preserving Operator Inequalities....Pages 180-190
The Band Extension on the Real Line as a Limit of Discrete Band Extensions, I. The Main Limit Theorem....Pages 191-220
Interpolating Sequences in the Maximal Ideal Space of H ∞ II....Pages 221-233
Operator Matrices with Chordal Inverse Patterns....Pages 234-251
Models and Unitary Equivalence of Cyclic Selfadjoint Operators in Pontrjagin Spaces....Pages 252-284
The von Neumann Inequality and Dilation Theorems for Contractions....Pages 285-291
Interpolation Problems, Inverse Spectral Problems and Nonlinear Equations....Pages 292-304
Extended Interpolation Problem in Finitely Connected Domains....Pages 305-327
Accretive Extensions and Problems on the Stieltjes Operator-Valued Functions Relations....Pages 328-347
Commuting Nonselfadjoint Operators and Algebraic Curves....Pages 348-371
All (?) About Quasinormal Operators....Pages 372-398
Back Matter....Pages 399-406

✦ Subjects

Science, general