PREFACE 1. CONVERGENT. Does the set of cyclic operators have a non-empty interior?... 2. WEIGHTED. Is every part of a weighted shift similar to a weighted shift?. . . . 3. INVARIANT. If an intransitive operator has an inverse, is its inverse also intransitive? 4. TRIANGULAR. Is every normal operator the sum of a diagonal operator and a compact one? 5. DILATED. Is every subnormal Toeplitz operat...

We define a new notion of entropy for operators on Fock spaces and positive definite multi-Toeplitz kernels on free semigroups. This is studied in connection with factorization theorems for (multi-Toeplitz, multi-analytic, etc.) operators on Fock spaces. These results lead to entropy inequalities and entropy formulas for positive definite multi-Toeplitz kernels on free semigroups (resp. multi-T...

Abstract We determine the eigenvalues of certain “fundamental” K -invariant Toeplitz type operators on weighted Bergman spaces over bounded symmetric domains $$D=G/K,$$ D = G / K , for irreducible -type...