Invariant Subsets and Homological Properties of Orlicz Modules over Group Algebras


ÜSTER R., Oztop S.

TAIWANESE JOURNAL OF MATHEMATICS, vol.24, no.4, pp.959-973, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 24 Issue: 4
  • Publication Date: 2020
  • Doi Number: 10.11650/tjm/190903
  • Journal Name: TAIWANESE JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Page Numbers: pp.959-973
  • Keywords: locally compact group, Orlicz space, invariant set, convex set, group algebra, Banach module, projectivity, injectivity, flatness, compact multiplier
  • Istanbul University Affiliated: Yes

Abstract

Let G be a locally compact group with left Haar measure. We study the closed convex left invariant subsets of L-Phi(G) and characterize affine mappings from the space of nonnegative functions in L-1(G) of norm 1 into L-Phi(G) spaces. We apply the results to the study of the multipliers of L-Phi(G). We also investigate the homological properties of L-Phi(G) as a Banach left L-1(G)-module such as projectivity, injectivity and flatness.