Beurling Type Theorem on the Hilbert Space Generated by a Positive Sequence |
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| Authors: | Wu Chang Hui Wang Zhi Jie Yu Tao |
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| Institution: | 1. School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, P. R. China;2. Department of Mathematics Physics and Information Engineering, Jiaxing University, Jiaxing 314001, P. R. China;3. School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, P. R. China |
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| Abstract: | Let H2(γ) be the Hilbert space over the bidisk D2 generated by a positive sequence γ={γnm}n,m ≥ 0. In this paper, we prove that the Beurling type theorem holds for the shift operator on H2(γ) with γ={γnm}n,m ≥ 0 satisfying certain series of inequalities. As a corollary, we give several applications to a class of classical analytic reproducing kernel Hilbert spaces over the bidisk D2. |
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| Keywords: | Beurling type theorem invariant subspace wandering subspace |
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