COMPLETELY CONTINUOUS COMPOSITION OPERATORS

被引：14

作者：

CIMA, JA

MATHESON, A

机构：

[1] MONTANA STATE UNIV,BOZEMAN,MT 59717

[2] LAMAR UNIV,DEPT MATH,BEAUMONT,TX 77710

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 1994年 / 344卷 / 02期

关键词：

COMPOSITION OPERATOR; COMPLETELY CONTINUOUS OPERATOR;

D O I：

10.2307/2154511

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A composition operator T(b)f = f o b is completely continuous on H-1 if and only if \b\ < 1 a.e. If the adjoint operator T(b)* is completely continuous on VMOA, then T(b) is completely continuous on H-1. Examples are given to show that the converse fails in general. Two results are given concerning the relationship between the complete continuity of an operator and of its adjoint in the presence of certain separability conditions on the underlying Banach space.

引用

页码：849 / 856

页数：8

共 15 条

[1] Banach S., 1932, OPERATIONS LINEAIRES
[2] A CHARACTERIZATION OF NON-DUNFORD-PETTIS OPERATORS ON L1
BOURGAIN, J
[J]. ISRAEL JOURNAL OF MATHEMATICS, 1980, 37 (1-2) : 48 - 53
[3] CONWAY JB, 1985, COURSE FUNCTIONAL AN
[4] DIESTEL J, 1984, SEQUENCES SERIES BAN
[5] DIESTEL J, 1980, CONT MATH, V2, P15
[6] SEQUENCES SPANNING A COMPLEX L1 SPACE
DOR, LE
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1975, 47 (02) : 515 - 516
[7] Dunford N., 1958, LINEAR OPERATORS 1
[8] CHARACTERIZATION OF BANACH-SPACES CONTAINING L
ROSENTHAL, HP
[J]. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1974, 71 (06) : 2411 - 2413
[9] ROSENTHAL HP, 1977, AM J MATH, V99, P803
[10] SARASON D, 1990, LECTURE NOTES MATH, V1511

← 1 2 →