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Commutants of Toeplitz operators with polynomial symbols on the Dirichlet space

Yong Chen|Young Joo Lee
대한수학회 (The Korean Mathematical Society)|2019.04|대한수학회논문집 (Communications of the KMS)|제34권 제2호|pp. 533-542|DOI 10.4134/CKMS.c180148

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참고문헌

키워드

Toeplitz operatorcommutantDirichlet space
주제분류수학

초록

We study commutants of Toeplitz operators acting on the Dirichlet space of the unit disk and prove that an operator in the Toeplitz algebra commuting with a Toeplitz operator with a nonconstant polynomial symbol must be a Toeplitz operator with an analytic symbol.

Abstract

We study commutants of Toeplitz operators acting on the Dirichlet space of the unit disk and prove that an operator in the Toeplitz algebra commuting with a Toeplitz operator with a nonconstant polynomial symbol must be a Toeplitz operator with an analytic symbol.

참고문헌 (15)

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  10. D. A. Stegenga, "Multipliers of the Dirichlet space", Illinois J. Math, 24(1), pp.113~139 (1980)
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