Transitive algebras and reductive algebras on reproducing analytic Hilbert spaces |
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Authors: | Guozheng Cheng Kai Wang |
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Affiliation: | School of Mathematical Sciences, Fudan University, Shanghai, 200433, China |
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Abstract: | In this paper, we consider the well-known transitive algebra problem and reductive algebra problem on vector valued reproducing analytic Hilbert spaces. For an analytic Hilbert space H(k) with complete Nevanlinna-Pick kernel k, it is shown that both transitive algebra problem and reductive algebra problem on multiplier invariant subspaces of H(k)⊗Cm have positive answer if the algebras contain all analytic multiplication operators. This extends several known results on the problems. |
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Keywords: | Transitive algebra property Reductive algebra property Fiber dimension Complete NP kernel |
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