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ON THE TOPOLOGICAL CENTRE OF L1(G/H)**

Part of: Abstract harmonic analysis

Published online by Cambridge University Press:  15 March 2012

R. RAISI TOUSI ,
R. A. KAMYABI-GOL  and
H. R. EBRAHIMI VISHKI
R. RAISI TOUSI*
Affiliation:
Department of Pure Mathematics, Ferdowsi University of Mashhad, PO Box 1159, Mashhad 91775, Iran (email: [email protected])
R. A. KAMYABI-GOL
Affiliation:
Department of Pure Mathematics, Ferdowsi University of Mashhad, PO Box 1159, Mashhad 91775, Iran Center of Excellence in Analysis on Algebraic Structures (CEAAS), PO Box 1159-91775, Mashhad, Iran (email: [email protected])
H. R. EBRAHIMI VISHKI
Affiliation:
Department of Pure Mathematics, Ferdowsi University of Mashhad, PO Box 1159, Mashhad 91775, Iran Center of Excellence in Analysis on Algebraic Structures (CEAAS), PO Box 1159-91775, Mashhad, Iran (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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Let G be a locally compact group and H be a compact subgroup of G. Using a general criterion established by Neufang [‘A unified approach to the topological centre problem for certain Banach algebras arising in abstract harmonic analysis’, Arch. Math.82(2) (2004), 164–171], we show that the Banach algebra L1(G/H) is strongly Arens irregular for a large class of locally compact groups.

Keywords

homogeneous spacetopological centreArens productfactorisation propertyMazur property

MSC classification

Secondary: 43A10: Measure algebras on groups, semigroups, etc.
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 86 , Issue 1 , August 2012 , pp. 119 - 125
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

References

[1]Folland, G. B., A Course in Abstract Harmonic Analysis (CRC Press, Boca Raton, FL, 1995).Google Scholar
[2]Hu, Z. and Neufang, M., ‘Decomposability of von Neumann algebras and the Mazur property of higher level’, Canad. J. Math. 58(4) (2006), 768–795.CrossRefGoogle Scholar
[3]Kamyabi-Gol, R. A., ‘The topological centre of L 1(K)**’, Sci. Math. Jpn. 62(1) (2005), 81–89.Google Scholar
[4]Kamyabi-Gol, R. A. and Tavallaei, N., ‘Convolution and homogeneous spaces’, Bull. Iranian Math. Soc. 35(1) (2009), 129–146.Google Scholar
[5]Lau, A. T., ‘Continuity of Arens multiplication on the dual space of bounded uniformly continuous functions on locally compact groups and topological semigroups’, Math. Proc. Cambridge Philos. Soc. 99 (1986), 273–283.CrossRefGoogle Scholar
[6]Lau, A. T. and Losert, V., ‘On the second conjugate algebra of L 1(G) of a locally compact group’, J. Lond. Math. Soc. 37 (1988), 445–460.Google Scholar
[7]Neufang, M., ‘A unified approach to the topological centre problem for certain Banach algebras arising in abstract harmonic analysis’, Arch. Math. 82(2) (2004), 164–171.CrossRefGoogle Scholar
[8]Neufang, M., ‘On a conjecture by Ghahramani-Lau and related problems concerning topological centres’, J. Funct. Anal. 224 (2005), 217–229.CrossRefGoogle Scholar
[9]Neufang, M., ‘Solution to a conjecture by Hofmeier-Wittstock’, J. Funct. Anal. 217(1) (2004), 171–180.CrossRefGoogle Scholar
[10]Reiter, H. and Stegeman, J. D., Classical Harmonic Analysis, 2nd edn (Oxford University Press, New York, 2000).Google Scholar