Transitive algebras and reductive algebras on reproducing analytic Hilbert spaces

被引：15
|
作者：
Cheng, Guozheng [1 ]
Guo, Kunyu [1 ]
Wang, Kai [1 ]
机构：
[1] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China
来源：
JOURNAL OF FUNCTIONAL ANALYSIS | 2010年 / 258卷 / 12期
关键词：
Transitive algebra property; Reductive algebra property; Fiber dimension; Complete NP kernel; NEVANLINNA-PICK KERNELS; INVARIANT SUBSPACES; FREDHOLM INDEX; COMMUTING OPERATORS; SHIFT; PAIR;
D O I：
10.1016/j.jfa.2010.01.021
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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) circle times C-m have positive answer if the algebras contain all analytic multiplication operators. This extends several known results on the problems. (C) 2010 Elsevier Inc. All rights reserved.
引用
收藏
页码：4229 / 4250
页数：22
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