Operator Theory and Related Topics de V. M. Adamyan

Operator Theory and Related Topics

V. M. Adamyan

Israel Gohberg

Myroslav L. Gorbachuk

Valentina Gorbachuk

Marinus A. Kaashoek

H. Langer

G. Popov

The present book is the second of the two volume Proceedings of the Mark Krein International Conference on Operator Theory and Applications. This conference, which was dedicated to the 90th Anniversary of the prominent mathematician Mark Krein, was held in Odessa, Ukraine from 18-22 August, 1997. The conference focused on the main ideas, methods, results, and achievements of M. G. Krein. This second volume is devoted to operator theory and related topics. It opens with the bibliography of M. G. Krein and a number of survey papers about his work. The main part of the book consists of original research papers presenting the state of the art in operator theory and its applications. The first volume of these proceedings, entitled Differential Operators and related Topics, concerns the other aspects of the conference. The two volumes will be of interest to a wide-range of readership in pure and applied mathematics, physics and engineering sciences. Table of Contents Preface. . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii Bibliography of Mark Grigorevich Krein . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix Review papers: M. G. Krein's Contributions to Prediction Theory H. Dym M. G. Krein's Contribution to the Moment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 AA Nudelman Research Papers: Solution of the Truncated Matrix Hamburger Moment Problem according to M. G. Krein . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Y. M. Adamyan and I. M. Tkachenko Extreme Points of a Positive Operator Ball . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 T. Ando M-accretive Extensions of Sectorial Operators and Krein Spaces . . . . . . . . . 67 Y. M. Arlinskii A Simple Proof of the Continuous Commutant Lifting Theorem . . . . . . . . . . 83 R. Bruzual and M.

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Review papers:.- M.G. Krein’s Contributions to Prediction Theory.- M.G. Krein’s Contribution to the Moment.- Research Papers:.- Solution of the Truncated Matrix Hamburger Moment Problem according to M.G. Krein.- Extreme Points of a Positive Operator Ball.- M-accretive Extensions of Sectorial Operators and Krein Spaces.- A Simple Proof of the Continuous Commutant Lifting Theorem.- The Outer Derivation Construction on the Algebra of Singular Integral Operators with General Coefficients in Weighted Spaces and its Applications.- Self-adjoint Operators with Inner Singularities and Pontryagin Spaces.- On the Uniform Convergence Theorem for Semigroups.- On Stochastic Integral, Wick Calculus and Generalized Stochastic Equations on Distribution Spaces of Non-gaussian Infinite Dimensional Analysis.- Bistrict Plus-operators in Krein Spaces and Dichotomous Behavior of Irreversible Dynamical Systems.- Singular Operator as a Parameter of Self-adjoint Extensions.- Few-body Krein’s Formula.- Linearization and Compact Perturbation of Self-adjoint Analytic Operator Functions.- Operator Interpretation of Resonances Generated by Some Operator Matrices.- Generalized Resolvents of Isometric Linear Relations in Pontryagin Spaces, I: Foundations.- A Termwise Differentiation in the Inductive Scales of the Locally Convex Spaces.- Operator Relations, Dynamical Systems, and Representations of a Class of Wick Algebras.- On Representations of Fn-algebras and their Applications.- Ergodic Theorems with Rates for R-times Integrated Solution Families.- Stochastic Equations in the Space of Formal Series: Convergence of Solution.- A Trigonometric Moment Problem for ?2.- Canonical Factorization of J-contractive-valued Functions.- Table of Contents of Volume I.