Recent Progress in Operator Theory

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.