Subnormal Toeplitz operators and the kernels of their self-commutators |
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Authors: | In Sung Hwang |
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Institution: | a Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Republic of Korea b Department of Mathematics, Seoul National University, Seoul 151-742, Republic of Korea |
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Abstract: | In this note we give a connection between subnormal Toeplitz operators and the kernels of their self-commutators. This is closely related to P.R. Halmos's Problem 5: Is every subnormal Toeplitz operator either normal or analytic? Our main theorem is as follows: If φ∈L∞ is such that φ and are of bounded type (that is, they are quotients of two analytic functions on the open unit disk) and if the kernel of the self-commutator of Tφ is invariant for Tφ then Tφ is either normal or analytic. |
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Keywords: | Toeplitz operators Subnormal Hyponormal Bounded type Self-commutator |
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