Taiwanese Journal of Mathematics

Invariant Subsets and Homological Properties of Orlicz Modules over Group Algebras

Rüya Üster and Serap Öztop

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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.

Article information

Source
Taiwanese J. Math., Volume 24, Number 4 (2020), 959-973.

Dates
Received: 24 March 2019
Revised: 8 September 2019
Accepted: 11 September 2019
First available in Project Euclid: 19 September 2019

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1568858572

Digital Object Identifier
doi:10.11650/tjm/190903

Mathematical Reviews number (MathSciNet)
MR4124553

Subjects
Primary: 43A15: $L^p$-spaces and other function spaces on groups, semigroups, etc. 43A22: Homomorphisms and multipliers of function spaces on groups, semigroups, etc. 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 46H25: Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)
Secondary: 43A20: $L^1$-algebras on groups, semigroups, etc.

Keywords
locally compact group Orlicz space invariant set convex set group algebra Banach module projectivity injectivity flatness compact multiplier

Citation

Üster, Rüya; Öztop, Serap. Invariant Subsets and Homological Properties of Orlicz Modules over Group Algebras. Taiwanese J. Math. 24 (2020), no. 4, 959--973. doi:10.11650/tjm/190903. https://projecteuclid.org/euclid.twjm/1568858572


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