Subnormal and Hyponormal Toeplitz Operators With Operator‐Valued Symbols

ABSTRACT

Let be a separable Hilbert space and let . We first show that is subnormal if and only if is subnormal for almost all . Next, given and a finite Blaschke–Potapov product in (the Cowen set of ), we consider the question of which subnormal Toeplitz operators are normal or analytic, and we give a sufficient condition for an affirmative answer. In addition, we extend a result of Nakazi–Takahashi for scalar‐valued Toeplitz operators with finite rank self‐commutators.