Rocky Mountain Journal of Mathematics

Invariantly complemented and amenability in Banach algebras related to locally compact groups

Ali Ghaffari and Somayeh Amirjan

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Abstract

In this paper, among other things, we show that there is a close connection between the existence of a bounded projection on some Banach algebras associated to a locally compact group~$G$ and the existence of a left invariant mean on $L^\infty (G)$. A necessary and sufficient condition is found for a locally compact group to possess a left invariant mean.

Article information

Source
Rocky Mountain J. Math., Volume 47, Number 2 (2017), 445-461.

Dates
First available in Project Euclid: 18 April 2017

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1492502545

Digital Object Identifier
doi:10.1216/RMJ-2017-47-2-445

Mathematical Reviews number (MathSciNet)
MR3635369

Zentralblatt MATH identifier
1371.43002

Subjects
Primary: 43A07: Means on groups, semigroups, etc.; amenable groups
Secondary: 43A22: Homomorphisms and multipliers of function spaces on groups, semigroups, etc.

Keywords
Amenability Banach algebra group algebra homomorphism operator projection weak$^*$ topology

Citation

Ghaffari, Ali; Amirjan, Somayeh. Invariantly complemented and amenability in Banach algebras related to locally compact groups. Rocky Mountain J. Math. 47 (2017), no. 2, 445--461. doi:10.1216/RMJ-2017-47-2-445. https://projecteuclid.org/euclid.rmjm/1492502545


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