On operators commuting with Toeplitz operators modulo the finite rank operators

被引：6

作者：

Gu, CX ^{[1
]}

机构：

[1] Calif Polytech State Univ San Luis Obispo, Coll Sci & Math, Dept Math, San Luis Obispo, CA 93407 USA

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2004年 / 215卷 / 01期

基金：

美国国家科学基金会;

关键词：

Toeplitz operator; Hankel operator; finite rank operator;

D O I：

10.1016/j.jfa.2004.01.011

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let X be a bounded linear operator on the Hardy space H-2 of the unit disk. We show that if X - T-0* XT0 is of finite rank for every inner function theta, then X = T-phi + F for some Toeplitz operator T-phi and some finite rank operator F on H-2. This solves a variant of an open question where the compactness replaces the finite rank conditions. (C) 2004 Elsevier Inc. All rights reserved.

引用

页码：178 / 205

页数：28

共 9 条

[1]

AXLER S, 1978, INTEGR EQUAT OPER TH, V1, P285

[2]

Brown A., 1964, Journal Fur die Reine und Angewandte Mathematik, V213, P89

[3] OPERATORS COMMUTING WITH TOEPLITZ OPERATORS MODULO COMPACT OPERATORS [J].