Multiplicative Isometries and Isometric Zero-Divisors

被引：22

作者：

Aleman, Alexandru ^{[1
]}

Duren, Peter ^{[2
]}

Martin, Maria J. ^{[3
]}

Vukotic, Dragan ^{[3
,4
]}

机构：

[1] Lund Univ, Dept Math, S-22100 Lund, Sweden

[2] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA

[3] Univ Autonoma Madrid, Dept Matemat, E-28049 Madrid, Spain

[4] Univ Autonoma Madrid, ICMAT CSIC UAM UC3M UCM, E-28049 Madrid, Spain

来源：

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES | 2010年 / 62卷 / 05期

关键词：

Banach spaces of analytic functions; Hardy spaces; Bergman spaces; Bloch space; Dirichlet space; Dirichlet-type spaces; pointwise multipliers; coefficient multipliers; isometrics; isometric zero-divisors; WEIGHTED BERGMAN SPACES; COMPOSITION OPERATORS; BLOCH SPACE; DIRICHLET SPACE; MULTIPLIERS;

D O I：

10.4153/CJM-2010-048-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For some Banach spaces of analytic functions in the unit disk (weighted Bergman spaces, Bloch space, Dirichlet-type spaces), the isometric pointwise multipliers are found to be unimodular constants. As a consequence, it is shown that none of those spaces have isometric zero-divisors. Isometric coefficient multipliers are also investigated.

引用

页码：961 / 974

页数：14

共 14 条

[1]

BROWN L, 1991, MICH MATH J, V38, P141

[2] Fractional integration, differentiation, and weighted Bergman spaces [J].