Recent Progress in Operator Theory

This and the previous volume of the OT series contain the proceedings of the Workshop on Operator Theory and its Applications, IWOTA 95, which was held at the University of Regensburg, Germany, July 31 to August 4, 1995. It was the eigth workshop of this kind. Following is a list of the seven previous workshops with reference to their proceedings: 1981 Operator Theory (Santa Monica, California, USA) 1983 Applications of Linear Operator Theory to Systems and Networks (Rehovot, Israel), OT 12 1985 Operator Theory and its Applications (Amsterdam, The Netherlands), OT 19 1987 Operator Theory and Functional Analysis (Mesa, Arizona, USA), OT 35 1989 Matrix and Operator Theory (Rotterdam, The Netherlands), OT 50 1991 Operator Theory and Complex Analysis (Sapporo, Japan), OT 59 1993 Operator Theory and Boundary Eigenvalue Problems (Vienna, Austria), OT 80 IWOTA 95 offered a rich programme on a wide range of latest developments in operator theory and its applications. The programme consisted of 6 invited plenary lectures, 54 invited special topic lectures and more than 100 invited session talks. About 180 participants from 25 countries attended the workshop, more than a third came from Eastern Europe. The conference covered different aspects of linear and nonlinear spectral prob­ lems, starting with problems for abstract operators up to spectral theory of ordi­ nary and partial differential operators, pseudodifferential operators, and integral operators. The workshop was also focussed on operator theory in spaces with indefinite metric, operator functions, interpolation and extension problems.

Inversion formulas for compressions of block-Toeplitz operators.- 1. Introduction.- 2. Main results.- 3. Inversion formulas for block-Toeplitz and block-Pick matrices.- 4. Inversion formulas for block-Toeplitz integral operators in 5-1 (0, a) (a < ?).- References.- Contractive linear relations in Pontryagin spaces.- 1. Introduction.- 2. Contractive linear relations.- 3. Regularization.- 4. Criteria for maximality.- 5. Properties of maximal contractive linear relations.- 6. Invariant subspaces.- References.- On a new algorithm for almost periodic factorization.- 1. Introduction.- 2. Known results.- 3. The reduction procedure.- 4. Matrices with regular Fourier spectra.- 5. Repeated use of the reduction procedure.- 6. Trinomial f.- 7. Block matrix generalizations.- 8. Final remarks.- References.- On the normal solvability of cohomological equations on compact topological spaces.- 1. Introduction.- 2. Dynamical lemmas.- 3. Proof of the Main Theorem.- 4. Appendix.- References.- On nonnegative realizations of rational matrix functions and nonnegative input-output systems.- 1. Introduction.- 2. Nonnegative realizations of rational matrix functions.- 3. Nonnegative input output systems.- 4. Appendix.- References.- On the geometric structure of regular dilations.- 1. Notations and preliminaries.- 2. The structure of regular and *-regular isometric dilations.- 3. Functional model and maximal function for a bicontraction having a *-regular dilation.- References.- On generalized interpolation and shift invariant maximal semidefinite subspaces.- 1. Introduction.- 2. Preliminaries.- 3. Generalized interpolation.- 4. The bitangential Nevanlinna-Pick problem.- References.- The sum of matrix Nevanlinna functions and self-adjoint extensions in exit spaces.- 1. Introduction.- 2. Nevanlinna pairs.- 3. Kre 6-1 n’s formula.- 4. The sum of Q-functions.- 5. The orthogonal sum of Sturm-Liouville operators.- 6. Schur complements of Q-functions.- 7. Nevanlinna functions and exit spaces.- References.- Properties of “derived” Hankel matrices.- 1. Introduction.- 2. Representations of m-derived Hankel matrices.- 3. Vandermonde factorization.- 4. Generating functions and Bezoutians.- 5. Triangular derived Hankel matrices.- References.- The probability that a (partial) matrix is positive semidefinite.- 1. Introduction.- 2. The case of full matrices.- 3. The case of partial matrices.- 4. The probability of the existence of a positive semidefinite completion.- References.- Factorization of lower triangular unitary operators with finite Kronecker index into elementary factors.- 1. Introduction.- 2. Unitary time varying systems.- 3. Observability and controllability of unitary time varying systems.- 4. A realization theorem.- 5. Cascade connection and factorization.- 6. Proof of Theorems 1.1 and 1.2.- 7. Main theorems for operators in the class LK.- References.- Fredholm theory of interpolation morphisms.- 1. Introduction.- 2. Fredholm theory in a paraalgebra of interpolation morphisms.- 3. Interpolation of Fredholm elements.- 4. Perturbation results for the real interpolation methods.- References.- Resolvents of symmetric operators and the degenerated Nevanlinna-Pick problem.- 1. Introduction.- 2. Straus extensions.- 3. The u-resolvents of S.- 4. The degenerated Nevanlinna-Pick problem.- 5. Explicit formulas.- References.- Perturbation of linear semigroups.- 1. Introduction.- 2. Essential spectral radius for perturbed semigroups.- References.- On the approximation of operators and the convergence of the spectra of the approximants.- 1. Introduction.- 2. The main result.- 3. Auxiliary results and proofs.- References.