INVARIANT SUBSPACES OF WEIGHTED BERGMAN SPACES IN INFINITELY MANY VARIABLES

被引：0

作者：

Dan, Hui ^{[1
]}

Guo, Kunyu ^{[2
,3
]}

Ni, Jiaqi ^{[2
,3
]}

机构：

[1] Sichuan Univ, Coll Math, Chengdu 610065, Peoples R China

[2] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China

[3] Northeast Normal Univ, Sch Math & Stat, Changchun 130024, Peoples R China

来源：

JOURNAL OF OPERATOR THEORY | 2023年 / 89卷 / 01期

关键词：

Invariant subspace; unitary equivalence; Hilbert module; Hardy space; weighted Bergman space; infinitely many variables; UNITARY EQUIVALENCE; HARDY SUBMODULES; RIGIDITY; OPERATOR;

D O I：

10.7900/jot.2021may18.2330

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper is concerned with polynomially generated multiplier invariant subspaces of the weighted Bergman space A2 beta in infinitely many variables. We completely classify these invariant subspaces under the uni-tary equivalence. Our results not only cover cases of both the Hardy space H2(D infinity 2 ) and the Bergman space A2(D infinity 2 ) in infinitely many variables, but also apply in finite variable setting.

引用

页码：183 / 204

页数：22

共 27 条

[1]

AGRAWAL OP, 1986, PAC J MATH, V121, P1

[2]

AHERN PR, 1970, J MATH MECH, V19, P963

[3] Fatou and brothers Riesz theorems in the infinite-dimensional polydisc [J].

Aleman, Alexandru ;

Olsen, Jan-Fredrik ;

Saksman, Eero .

JOURNAL D ANALYSE MATHEMATIQUE, 2019, 137 (01) :429-447

[4]

Atiyah M., 1969, INTRO COMMUTATIVE AL

[5]

BERCOVICI H., 1985, CBMS REGIONAL C SER, V56

[6]

BEREZANSKII Y.M., 1986, TRANSL MATH MONOGR, V63

[7]

CHEN X., 2003, ANAL HILBERT MODULES, V433

[8]

CHEN XM, 1992, HOUSTON J MATH, V18, P117

[9]

COLE BJ, 1986, P LOND MATH SOC, V53, P112

[10] The periodic dilation completeness problem: cyclic vectors in the Hardy space over the infinite-dimensional polydisk [J].

Dan, Hui ;

Guo, Kunyu .

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2021, 103 (01) :1-34

← 1 2 3 →