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HOMOMORPHISMS OF $\ell ^{1}$-MUNN ALGEBRAS AND APPLICATIONS TO SEMIGROUP ALGEBRAS

Part of: Topological algebras, normed rings and algebras, Banach algebras Abstract harmonic analysis

Published online by Cambridge University Press:  02 April 2015

MAEDEH SOROUSHMEHR
MAEDEH SOROUSHMEHR*
Affiliation:
Department of Mathematics, Faculty of Mathematical Science and Computer, Kharazmi University, 50 Taleghani Avenue, 64518, Tehran, Iran email std_soroushmehr@khu.ac.ir
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Abstract

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In this paper, for an arbitrary $\ell ^{1}$-Munn algebra $\mathfrak{A}$ over a Banach algebra $A$ with a sandwich matrix $P$, we characterise all homomorphisms from $\mathfrak{A}$ to a commutative Banach algebra $B$. Especially, we study the character space of this algebra. Then, as an application, its character amenability is investigated. Finally, we apply these results to certain semigroups, which are called Rees matrix semigroups.

Keywords

Banach algebrasemigroupsemigroup algebrahomomorphismcharacter spaceamenabilitycharacter amenability

MSC classification

Primary: 46H05: General theory of topological algebras 43A22: Homomorphisms and multipliers of function spaces on groups, semigroups, etc.
Secondary: 43A07: Means on groups, semigroups, etc.; amenable groups 43A20: $L^1$-algebras on groups, semigroups, etc.
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 92 , Issue 1 , August 2015 , pp. 115 - 122
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

References

Arens, R., ‘Operations induced in function classes’, Monatsh. Math. 55 (1951), 1–19.CrossRefGoogle Scholar
Arens, R., ‘The adjoint of a bilinear operation’, Proc. Amer. Math. Soc. 2 (1951), 839–848.CrossRefGoogle Scholar
Clifford, A. H. and Preston, G. B., The Algebraic Theory of Semigroups, Vol. I, Mathematical Surveys, 7 (American Mathematical Society, Providence, RI, 1961).CrossRefGoogle Scholar
Dales, H. G., Lau, A. T.-M. and Strauss, D., ‘Banach algebras on semigroups and their compactifications’, Mem. Amer. Math. Soc. 205 (2010), 1–165.Google Scholar
Esslamzadeh, G. H., ‘Banach algebra structure and amenability of a class of matrix algebras with applications’, J. Funct. Anal. 161 (1999), 364–383.CrossRefGoogle Scholar
Esslamzadeh, G. H., ‘Duals and topological center of a class of matrix algebras with applications’, Proc. Amer. Math. Soc. 128 (2000), 3493–3503.CrossRefGoogle Scholar
Hu, Z., Sangari-Monfared, M. and Traynor, T., ‘On character amenable Banach algebras’, Studia Math. 193 (2009), 53–78.CrossRefGoogle Scholar
Kaniuth, E., Lau, A. T.-M. and Pym, J., ‘On 𝜑-amenability of Banach algebras’, Math. Proc. Cambridge Philos. Soc. 144 (2008), 85–96.CrossRefGoogle Scholar
Munn, W. D., ‘On semigroup algebras’, Math. Proc. Cambridge Philos. Soc. 51 (1955), 1–15.CrossRefGoogle Scholar
Sangari-Monfared, M., ‘Character amenability of Banach algebras’, Math. Proc. Cambridge Philos. Soc. 144 (2008), 697–706.CrossRefGoogle Scholar
Soroushmehr, M., ‘Ultrapowers of ℓ 1-Munn algebras and their application to semigroup algebras’, Bull. Aust. Math. Soc. 86 (2012), 424–429.CrossRefGoogle Scholar
Soroushmehr, M., ‘Weighted Rees matrix semigroup algebras and their applications’, Arch. Math. (Basel) 100(2) (2013), 139–147.CrossRefGoogle Scholar