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ARENS REGULARITY AND AMENABILITY OF LAU PRODUCT OF BANACH ALGEBRAS DEFINED BY A BANACH ALGEBRA MORPHISM

Part of: Topological algebras, normed rings and algebras, Banach algebras

Published online by Cambridge University Press:  31 July 2012

S. J. BHATT  and
P. A. DABHI
S. J. BHATT
Affiliation:
Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar 388120, Gujarat, India (email: [email protected])
P. A. DABHI*
Affiliation:
Department of Mathematics, Sardar Patel University, Vallabh Vidyanagar 388120, Gujarat, India (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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Given a morphism T from a Banach algebra ℬ to a commutative Banach algebra 𝒜, a multiplication is defined on the Cartesian product space 𝒜×ℬ perturbing the coordinatewise product resulting in a new Banach algebra 𝒜×Tℬ. The Arens regularity as well as amenability (together with its various avatars) of 𝒜×Tℬ are shown to be stable with respect to T.

Keywords

perturbation of Cartesian productArens regularityamenabilityweak amenabilityapproximate amenabilityapproximate weak amenabilitycyclic amenabilityapproximate cyclic amenabilityφ-inner amenabilitycharacter amenability

MSC classification

Secondary: 46H05: General theory of topological algebras
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 87 , Issue 2 , April 2013 , pp. 195 - 206
Copyright
©2012 Australian Mathematical Publishing Association Inc.

References

[1]Arens, R., ‘Operations induced in function classes’, Monatsh. Math. 55 (1951), 1–19.CrossRefGoogle Scholar
[2]Arens, R., ‘The adjoint of a bilinear operation’, Proc. Amer. Math. Soc. 2 (1951), 839–848.CrossRefGoogle Scholar
[3]Dales, H. G., Banach Algebras and Automatic Continuity, London Mathematical Society Monographs New Series, 24 (Oxford University Press, Oxford, 2000).Google Scholar
[4]Davidson, K. R., C *-Algebras by Example, Text and Readings in Mathematics, 11 (Hindustan Book Agency, New Delhi, 1996).CrossRefGoogle Scholar
[5]Ebrahimi Vishki, H. R. & Khoddami, A. R., ‘Character inner amenability of certain Banach algebras’, arXiv:1007.1654v1 [math.FA], 9 July 2010.Google Scholar
[6]Esslamzadeh, G. H. & Shojaee, B., ‘Approximate weak amenability of Banach algebras’, arXiv:0908.3577v2 [math.FA], 18 Jan. 2011.Google Scholar
[7]Hu, Z., Monfared, M. S. & Traynor, T., ‘On character amenable Banach algebras’, Studia Math. 193(1) (2009), 53–78.CrossRefGoogle Scholar
[8]Kaniuth, E., A Course in Commutative Banach Algebras (Springer, New York, 2009).CrossRefGoogle Scholar
[9]Kaniuth, E., Lau, A. T.-M. & Pym, J., ‘On character amenability of Banach algebras’, J. Math. Anal. Appl. 344(2) (2008), 942–955.CrossRefGoogle Scholar
[10]Kaniuth, E., Lau, A. T.-M. & Pym, J., ‘On φ-amenability of Banach algebras’, Math. Proc. Cambridge Philos. Soc. 144(1) (2008), 85–96.CrossRefGoogle Scholar
[11]Lau, A. T.-M., ‘Analysis on a class of Banach algebras with applications to harmonic analysis on locally compact groups and semigroups’, Fund. Math. 118 (1983), 161–175.Google Scholar
[12]Lau, A. T.-M. & Ludwig, J., ‘Fourier–Stieltjes algebra of topological group’, Adv. Math. 229(3) (2012), 2000–2023.CrossRefGoogle Scholar
[13]Monfared, M. S., ‘On certain products of Banach algebras with application to Harmonic analysis’, Studia Math. 178(3) (2007), 277–294.CrossRefGoogle Scholar
[14]Monfared, M. S., ‘Character amenability of Banach algebras’, Math. Proc. Cambridge Philos. Soc. 144(3) (2008), 697–706.CrossRefGoogle Scholar
[15]Runde, V., Lectures on Amenability, Lectures Notes in Mathematics, 1774 (Springer, Berlin–Heidelberg–New York, 2002).CrossRefGoogle Scholar
[16]Takesaki, M., ‘Duality and von Neumann algebras’, in: Lectures on Operator Algebras, Lecture Notes in Mathematics, 247 (Springer, Berlin), pp. 665–779.CrossRefGoogle Scholar