ScholarWorks@성균관대학교

초록

In this paper we consider the subnormality of block Toeplitz operators T Phi, where Phi is an n x n matrix-valued function on the unit circle T$\mathbb{T}$ of the form Phi=Q Phi & lowast;(QisafiniteBlaschke-Potapovproduct)$\Phi =Q\Phi {<}^{>}\ast (Q\text{is}\text{a}\text{finite}\text{Blaschke-Potapov}\text{product})$This is related to a matrix-valued version of Halmos' Problem 5 and the Nakazi-Takahashi Theorem. We ask whether T Phi is either normal or analytic if T Phi is subnormal, where Phi is of the above form. We give answers to this problem for different cases of the symbol. Moreover, we provide a sufficient condition for the answer to be affirmative when Phi* is not of bounded type.

키워드