Isometric isomorphisms of Beurling algebras

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:438

Article

Zadeh, Safoura¹ 

[1] Univ Manitoba, Dept Math, 342 Machray Hall,186 Dysart Rd, Winnipeg, MB R3T 2N2, Canada

关键词: Locally compact groups;    Beurling algebras;    Isometric isomorphisms;    Arens product;   

DOI  :  10.1016/j.jmaa.2016.01.060

来源: Elsevier

【 摘 要 】

Let G and H be locally compact groups with continuous weights omega(1) and omega(2) respectively, such that omega(i)(e(i)) = 1, i = 1,2. In this article we show that if M(G, omega(1)) (the weighted measure algebra on G) is isometrically algebra isomorphic to M(H, omega(1)), then the underlying weighted groups are isomorphic, i.e. there exists an isomorphism of topological groups phi : G -> H such that omega(1)/omega(2) omicron phi, is multiplicative. Similarly, we show that any weighted locally compact group (G, omega) is completely determined by its Beurling group algebra L-1(G, omega), LUC(G, omega(-1))* and L-1(G, omega)**, when the two last algebras are equipped with an Arens product. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free