Bulletin of the Belgian Mathematical Society - Simon Stevin

Module Maps and Invariant Subsets of Banach Modules of Locally Compact Groups

Hawa Alsanousi Hamouda

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Abstract

For a locally compact group $G$, Lau and Ghaffari provided many results about $G$-invariant subsets of $G$-modules, and the relationship between $G$-module maps, $L^1(G)$-module maps and $M(G)$- module maps. In both papers their results were specified for one module action. In this paper we extend many of their results to arbitrary Banach $G$-modules and $G$-module maps.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 21, Number 2 (2014), 253-261.

Dates
First available in Project Euclid: 20 May 2014

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1400592623

Digital Object Identifier
doi:10.36045/bbms/1400592623

Mathematical Reviews number (MathSciNet)
MR3211014

Zentralblatt MATH identifier
1295.43005

Subjects
Primary: 43A20: $L^1$-algebras on groups, semigroups, etc. 43A22: Homomorphisms and multipliers of function spaces on groups, semigroups, etc. 46H25: Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)

Keywords
locally compact groups group algebras measure algebras Banach modules module homomorphisms invariant subsets of Banach modules

Citation

Hamouda, Hawa Alsanousi. Module Maps and Invariant Subsets of Banach Modules of Locally Compact Groups. Bull. Belg. Math. Soc. Simon Stevin 21 (2014), no. 2, 253--261. doi:10.36045/bbms/1400592623. https://projecteuclid.org/euclid.bbms/1400592623


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