First results on spectrally bounded operators

被引：27

作者：

Mathieu, M ^{[1
]}

Schick, GJ ^{[1
]}

机构：

[1] Queens Univ Belfast, Dept Pure Math, Belfast BT7 1NN, Antrim, North Ireland

来源：

STUDIA MATHEMATICA | 2002年 / 152卷 / 02期

关键词：

spectral structure on Banach spaces; spectrally bounded operators; Banach algebras; automatic continuity;

D O I：

10.4064/sm152-2-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A linear mapping T from a subspace E of a Banach algebra into another Banach algebra is defined to be spectrally bounded if there is a constant M greater than or equal to 0 such that r(Tx) less than or equal to Mr(x) for all x is an element of E, where r((.)) denotes the spectral radius. We study some basic properties of this class of operators, which are sometimes analogous to, sometimes very different from, those of bounded operators between Banach spaces.

引用

页码：187 / 199

页数：13

共 22 条

[11] SPECTRALLY BOUNDED GENERALIZED INNER DERIVATIONS
CURTO, R
MATHIEU, M
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1995, 123 (08) : 2431 - 2434
[12] MATHIEU M, IN PRESS J OPERATOR
[13] Mathieu M., 1994, Banach Center Publ., V30, P237
[14] PEARCY C, 1967, MICH MATH J, V14, P453
[15] DERIVATIONS, COMMUTATORS AND RADICAL
PTAK, V
[J]. MANUSCRIPTA MATHEMATICA, 1978, 23 (04) : 355 - 362
[16] PTAK V, 1979, P EDINBURGH MATH SOC, V22, P207, DOI 10.1017/S0013091500016357
[17] RODRIGUEZ A, 1985, J FUNCT ANAL, V60, P1
[18] SCHICK GJ, 2001, THESIS QUEENS U BELF
[19] Semrl P, 1998, Q J MATH, V49, P87
[20] Invertibility preserving linear maps on L(X)
Sourour, AR
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1996, 348 (01) : 13 - 30

← 1 2 3 →