Theoretical analysis characterizes subnormality and conditions for normality in operator-valued Toeplitz operators, extending classical commutativity theorems to broader Hilbert spaces.
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.
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Abhinand et al. (2026) studied this question.
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