Multinorms and Approximate Amenability of Weighted Group Algebras. (23rd February 2014)

• Record Type: Journal Article
• Authors: Ghaderkhani, Saman
• Other Names: Lin H. Academic Editor.; You H. Academic Editor.; Zhao C.-J. Academic Editor.
• Is Part Of: Chinese journal of mathematics. Volume 2014(2014)
• Publication Date: 2014-02-23
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals
• DOI: 10.1155/2014/410262
• Languages: English
• ISSNs: 2314-8071

Abstract

Abstract : Let G be a locally compact group, and takep, q with1 ≤ p, q < ∞ . We prove that, for any left( p, q ) -multiinvariant functional onL ∞ ( G ) and for any weight functionω ≥ 1 onG, the approximate amenability of the Banach algebraL 1 ( G, ω ) implies the left( p, q ) -amenability ofG, but in general the opposite is not true. Our proof uses the notion of multinorms. We also investigate the approximate amenability ofM ( G, ω ) .