CROSS COMMUTATORS ON BACKWARD SHIFT INVARIANT SUBSPACES OVER THE BIDISK II

被引：0

作者：

Izuchi, Kei Ji ^{[1
]}

Izuchi, Kou Hei ^{[2
]}

机构：

[1] Niigata Univ, Dept Math, Niigata 9502181, Japan

[2] Yamaguchi Univ, Fac Educ, Yamaguchi 7538513, Japan

来源：

JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY | 2012年 / 49卷 / 01期

基金：

日本学术振兴会;

关键词：

backward shift invariant subspace; invariant subspace; Hardy space; cross commutator;

D O I：

10.4134/JKMS.2012.49.1.139

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the previous paper, we gave a characterization of backward shift invariant subspaces of the Hardy space over the bidisk on which [S(z)(n), S(w)*] for a positive integer n >= 2. In this case, it holds that S(z)(n) = cI for some c is an element of C. In this paper, it is proved that if [S(phi), S(w)*] = 0 and phi is an element of H(infinity)(Gamma(z)), then S(phi) = cI for some c is an element of C.

引用

页码：139 / 151

页数：13

共 11 条

[1]

[Anonymous], 1969, FUNCTION THEORY POLY

[2]

Bercovici H., 1988, Mathematical Surveys and Monographs, V26

[3] ON 2 PROBLEMS CONCERNING LINEAR TRANSFORMATIONS IN HILBERT SPACE [J].

BEURLING, A .

ACTA MATHEMATICA, 1949, 81 (02) :239-255

[4]

Chen X., 2003, Analytic Hilbert modules

[5]

Izuchi K, 2004, J OPERAT THEOR, V51, P361

[6]

Izuchi K., 2004, Acta Sci. Math, V70, P727

[7]

Izuchi KJ, 2006, ACTA SCI MATH, V72, P251

[8]

IZUCHI KJ, COMMUTATIVITY 2 VARI

[9] THE VALIDITY OF BEURLING THEOREMS IN POLYDISCS [J].

MANDREKAR, V .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1988, 103 (01) :145-148

[10]

NIKOLSKII NK, 1986, TREATISE SHIFT OPERA

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