A Class of Operators Similar to the Shift on H 2(G) |
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Authors: | Zhijian Qiu |
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Affiliation: | (1) Research Institute of Mathematics, HanShan Normal University, ChaoZhou, GaungDong, 521041, China |
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Abstract: | For a compact subset K in the complex plane, let A(K) denote the algebra of all functions continuous on K and analytic on K° and let R(K) denote the uniform closure of the rational functions with poles off K. Let G is a bounded open subset whose complement in the plane has a finite number of components. Suppose that and every function in H∞(G) is the pointwise limit of a bounded sequence of functions in . The purpose of this paper is to characterize all subnormal operators similar to Mz, the operator of multiplication by the independent variable z on the Hardy space H2(G). We also characterize all bounded linear operators that are unitarily equivalent to Mz in the case when each of the components of G is simply connected. In particular, our similarity result extends a well-known result of W. Clary on the unit disk to multiply connected domains. |
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Keywords: | Primary 47B20 Secondary 30H05 30E10 46E15 |
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