MULTIPLIERS WITH CLOSED RANGE ON REGULAR COMMUTATIVE BANACH-ALGEBRAS

被引：5

作者：

AIENA, P ^{[1
]}

LAURSEN, KB ^{[1
]}

机构：

[1] UNIV COPENHAGEN,INST MATEMAT,DK-2100 COPENHAGEN,DENMARK

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 1994年 / 121卷 / 04期

关键词：

D O I：

10.2307/2161212

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Conditions equivalent with closure of the range of a multiplier T, defined on a commutative semisimple Banach algebra A, are studied. A main result is that if A is regular then T2A is closed if and only if T is a product of an idempotent and an invertible. This has as a consequence that if A is also Tauberian then a multiplier with closed range is injective if and only if it is surjective. Several aspects of Fredholm theory and Kato theory are covered. Applications to group algebras are included.

引用

页码：1039 / 1048

页数：10

共 15 条

[1]

AIENA P, 1993, REND CIRC MAT PALERM, V33, P155

[2]

Barnes B.A., 1982, RIESZ FREDHOLM THEOR

[3]

Caradus S.R., 1974, CALKIN ALGEBRAS ALGE

[4] MULTIPLIERS OF SEGAL ALGEBRAS [J].

DUTTA, M ;

TEWARI, UB .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1978, 72 (01) :121-124

[5]

ESCHMEIER J, UNPUB MULTIPLIERS NA

[6] WHEN IS MU'L1 CLOSED [J].

GLICKSBERT, I .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1971, 160 (NOCT) :419-+

[7]

Host B., 1978, ANN I FOURIER GRENOB, V28, P143

[8] ON COMPACT MULTIPLIERS OF BANACH-ALGEBRAS [J].

KAMOWITZ, H .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1981, 81 (01) :79-80

[9]

LARSEN R, 1971, THEORY MULTIPLIERS

[10] LOCAL SPECTRAL PROPERTIES OF MULTIPLIERS ON BANACH-ALGEBRAS [J].

LAURSEN, KB ;

NEUMANN, MM .

ARCHIV DER MATHEMATIK, 1992, 58 (04) :368-375

← 1 2 →