Operator Theory and Interpolation

Systems and control theories use sophisticated operator theoretical methods. They also provide new ideas and problems in operator theory. As a consequence, the biannual MTNS (Mathematical Theory of Networks and Systems) conference is attended by many operator theorists. At the initiative of J.W. Helton and I. Gohberg, an International Workshop on Operator Theory and Applications (IWOTA) has been organized since the early 80s, as a satellite of MTNS. The articles in this volume originated from the IWOTA conference held at Indiana University, Bloomington, in June 1996. They represent most of the areas that were discussed at the workshop with some emphasis on modern interpolation theory, a topic which has seen much progress in recent years. The contributions were, as usual, subject to a thorough refereeing process and will bring the reader to the forefront of current research in this area.

Inhalt
Classical Nevanlinna-Pick Interpolation with Real Interpolation Points.- The Abstract Interpolation Problem and Commutant Lifting: A Coordinate-free Approach.- On Classes of Realizable Operator-valued R-functions.- Submodules of L2(TN).- Kolmogorov Decompositions and the Realization of Time Dependent Systems.- Hankel Forms and Operators in Hardy Spaces with Two Szego Weights.- The Structured Norm of a Hilbert Space operator with respect to a Given Algebra of Operators.- Order Preserving Operator Function via Furuta Inequality.- On a Nonlinear Causal Commutant Lifting Theorem.- Parametrization of Solutions of the Nehari Problem and Nonorthogonal Dynamics.- On Zeros of Defining Functions for some Hilbert Spaces of Polynomials.- One or Two Parameter Algebraic Scattering Systems and the Commutant Lifting Theorem.- On Interpolation Problems in the Complex Right Half Plane.- Maximum Entropy Truncable Positive Definite Sequences of Analytic Toeplitz Operators.- Subdecomposable Operators and Rationally Invariant Subspaces.