Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Herz-Schur multipliers
and weakly almost periodic functions
on locally compact groups


Author: Guangwu Xu
Journal: Trans. Amer. Math. Soc. 349 (1997), 2525-2536
MSC (1991): Primary 43A30, 43A60, 43A46; Secondary 22D05, 22D25
MathSciNet review: 1373647
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: For a locally compact group $G$ and $1<p<\infty $, let $A_{p}(G)$ be the Herz-Figà-Talamanca algebra and $B_{p}(G)$ the Herz-Schur multipliers of $G$, and $MA_{p}(G)$ the multipliers of $A_{p}(G)$. Let $W(G)$ be the algebra of continuous weakly almost periodic functions on $G$. In this paper, we show that (1), if $G$ is a noncompact nilpotent group or a noncompact [IN]-group, then $W(G)/B_{p}(G)^{-}$ contains a linear isometric copy of $l^{\infty }({\mathbb {N}})$; (2), for a noncommutative free group $F, B_{p}(F)$ is a proper subset of ${MA_{p}(F)\cap {W(F)}}$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 43A30, 43A60, 43A46, 22D05, 22D25

Retrieve articles in all journals with MSC (1991): 43A30, 43A60, 43A46, 22D05, 22D25


Additional Information

Guangwu Xu
Affiliation: Department of Mathematics, State University of New York at Buffalo, Buffalo, New York 14214-3093
Address at time of publication: Department of Mathematical Sciences, University of Alberts, Edmonton, AB, T6G 2G1, Canada
Email: gxu@vega.math.ualberta.ca

DOI: http://dx.doi.org/10.1090/S0002-9947-97-01733-9
PII: S 0002-9947(97)01733-9
Received by editor(s): November 29, 1994
Received by editor(s) in revised form: January 29, 1996
Article copyright: © Copyright 1997 American Mathematical Society