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- W2951433313 abstract "In this paper we are concerned with hyponormality and subnormality of block operators acting on the vector-valued Hardy space $H^2_{mathbb{C}^n}$ of the unit circle. Firstly, we establish a tractable and explicit criterion on the hyponormality of block operators having bounded type symbols via the triangularization theorem for compressions of the shift operator. Secondly, we consider the gap between hyponormality and subnormality for block operators. This is closely related to Halmos's Problem 5: Is every subnormal operator either normal or analytic? We show that if $Phi$ is a matrix-valued rational function whose co-analytic part has a coprime factorization then every hyponormal operator $T_{Phi}$ whose square is also hyponormal must be either normal or analytic. Thirdly, using the subnormal theory of block operators, we give an answer to the following Toeplitz completion problem: Find the unspecified entries of the partial block matrix $$A:=[U^*& ? ?&U^*] $$ so that $A$ becomes subnormal, where $U$ is the unilateral shift on $H^2$." @default.
- W2951433313 created "2019-06-27" @default.
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- W2951433313 date "2012-01-28" @default.
- W2951433313 modified "2023-09-27" @default.
- W2951433313 title "Hyponormality and Subnormality of Block Toeplitz Operators" @default.
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