Reducing subspaces of compressed analytic Toeplitz operators on the Hardy space |
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Authors: | Chan Kit C Seubert Steven M |
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Institution: | (1) Department of Mathematics and Statistics, Bowling Green State University, 43403 Bowling Green, Ohio, USA |
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Abstract: | In this paper we discuss necessary conditions and sufficient conditions for the compression of an analytic Toeplitz operator onto a shift coinvariant subspace to have nontrivial reducing subspaces. We give necessary and sufficient conditions for the kernel of a Toeplitz operator whose symbol is the quotient of two inner functions to be nontrivial and obtain examples of reducing subspaces from these kernels. Motivated by this result we give necessary conditions and sufficient conditions for the kernel of a Toeplitz operator whose symbol is the quotient of two inner functions to be nontrivial in terms of the supports of the two inner functions. By studying the commutant of a compression, we are able to give a necessary condition for the existence of reducing subspaces on certain shift coinvariant subspaces. |
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Keywords: | 46E20 47A15 47A20 |
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