ORDER STRUCTURE, MULTIPLIERS, AND GELFAND REPRESENTATION OF VECTOR-VALUED FUNCTION ALGEBRAS

被引：1

作者：

Arhippainen, Jorma ^{[1
]}

Kauppi, Jukka ^{[1
]}

Mattas, Jussi ^{[1
]}

机构：

[1] Univ Oulu, Dept Math Sci, POB 3000, SF-90014 Oulu, Finland

来源：

BANACH JOURNAL OF MATHEMATICAL ANALYSIS | 2017年 / 11卷 / 01期

关键词：

vector-valued function algebra; C*-Segal algebra; multiplier module; order unitization; Gelfand representation; ASTERISK-SEGAL ALGEBRAS; BANACH-ALGEBRAS; 1ST KIND; IDEALS; UNIT;

D O I：

10.1215/17358787-3784682

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We continue the study begun by the third author of C*-Segal algebra-valued function algebras with an emphasis on the order structure. Our main result is a characterization theorem for C*-Segal algebra-valued function algebras with an order unitization. As an intermediate step, we establish a function algebraic description of the multiplier module of arbitrary Segal algebra-valued function algebras. We also consider the Gelfand representation of these algebras in the commutative case.

引用

页码：207 / 222

页数：16