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THE MODULUS OF WEAKLY COMPACT MULTIPLIERS ON THE BANACH ALGEBRA L1(𝒢)** OF A LOCALLY COMPACT GROUP

Part of: Abstract harmonic analysis

Published online by Cambridge University Press:  25 January 2012

MOHAMMAD JAVAD MEHDIPOUR
MOHAMMAD JAVAD MEHDIPOUR*
Affiliation:
Department of Mathematics, Shiraz University of Technology, Shiraz 71555-313, Iran (email: [email protected])
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Abstract

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In this paper we give a necessary and sufficient condition under which the answer to the open problem raised by Ghahramani and Lau (‘Multipliers and modulus on Banach algebras related to locally compact groups’, J. Funct. Anal. 150 (1997), 478–497) is positive.

Keywords

locally compact groupweakly compact multipliermodulus of operator

MSC classification

Secondary: 43A22: Homomorphisms and multipliers of function spaces on groups, semigroups, etc.
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 86 , Issue 2 , October 2012 , pp. 315 - 321
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

References

[1]Aguayo, J. and Sanchez, J., ‘Weakly compact operators and the strict toplogies’, Bull. Aust. Math. Soc. 39 (1989), 353–359.CrossRefGoogle Scholar
[2]Akemann, C. A., ‘Some mapping properties of the group algebras of a compact group’, Pacific J. Math. 22 (1967), 1–8.CrossRefGoogle Scholar
[3]Aliprantis, C. D. and Burkinshaw, O., Positive Operator (Academic Press, New York, London, 1985).Google Scholar
[4]Folland, G. B., A Course in Abstract Harmonic Analysis (CRC Press, Boca Raton, FL, 1995).Google Scholar
[5]Ghahramani, F. and Lau, A. T., ‘Isomorphisms and multipliers on second dual algebras of Banach algebras’, Math. Proc. Cambridge Philos. Soc. 111 (1992), 161–168.CrossRefGoogle Scholar
[6]Ghahramani, F. and Lau, A. T., ‘Multipliers and ideals in second conjugate algebras related to locally compact groups’, J. Funct. Anal. 132 (1995), 170–191.CrossRefGoogle Scholar
[7]Ghahramani, F. and Lau, A. T., ‘Multipliers and modulus on Banach algebras related to locally compact groups’, J. Funct. Anal. 150 (1997), 478–497.CrossRefGoogle Scholar
[8]Ghahramani, F., Lau, A. T. and Losert, V., ‘Isometric isomorphisms between Banach algebras related to locally compact groups’, Trans. Amer. Math. Soc. 321 (1990), 273–283.CrossRefGoogle Scholar
[9]Hewitt, E. and Ross, K., Abstract Harmonic Analysis I (Springer, New York, 1970).Google Scholar
[10]Kaniuth, E., A Course in Commutative Banach Algebras (Springer, New York, 2009).CrossRefGoogle Scholar
[11]Losert, V., ‘Weakly compact multipliers on group algebras’, J. Funct. Anal. 213 (2004), 466–472.CrossRefGoogle Scholar
[12]Murphy, G. J., C*-Algebras and Operator Theory (Academic Press, Boston, 1990).Google Scholar
[13]Sakai, S., ‘Weakly compact operators on operator algebras’, Pacific J. Math. 14 (1964), 659–664.CrossRefGoogle Scholar