Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-24T03:55:07.186Z Has data issue: false hasContentIssue false
  • English
  • Français

COMPACT LEFT MULTIPLIERS ON BANACH ALGEBRAS RELATED TO LOCALLY COMPACT GROUPS

Part of: Topological algebras, normed rings and algebras, Banach algebras Special classes of linear operators Abstract harmonic analysis

Published online by Cambridge University Press:  13 March 2009

M. J. MEHDIPOUR  and
R. NASR-ISFAHANI
M. J. MEHDIPOUR
Affiliation:
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran (email: [email protected])
R. NASR-ISFAHANI*
Affiliation:
Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We deal with the dual Banach algebras for a locally compact group G. We investigate compact left multipliers on , and prove that the existence of a compact left multiplier on is equivalent to compactness of G. We also describe some classes of left completely continuous elements in .

Keywords

Arens productcompact operatorleft completely continuous elementleft multiplierlocally compact group

MSC classification

Secondary: 43A15: $L^p$-spaces and other function spaces on groups, semigroups, etc. 46H05: General theory of topological algebras 47B48: Operators on Banach algebras 47B07: Operators defined by compactness properties
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 79 , Issue 2 , April 2009 , pp. 227 - 238
Copyright
Copyright © Australian Mathematical Society 2009

References

[1] Akemann, C. A., ‘Some mapping properties of the group algebras of a compact group’, Pacific J. Math. 22 (1967), 1–8.CrossRefGoogle Scholar
[2] 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
[3] Ghahramani, F. and Lau, A. T., ‘Multipliers and ideal in second conjugate algebras related to locally compact groups’, J. Funct. Anal. 132 (1995), 170–191.CrossRefGoogle Scholar
[4] 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
[5] 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
[6] Hewitt, E. and Ross, K., Abstract Harmonic Analysis I (Springer, New York, 1970).Google Scholar
[7] Hewitt, E. and Stromberg, K., Real and Abstract Analysis (Springer, New York, 1975).Google Scholar
[8] Isik, N., Pym, J. and Ülger, A., ‘The second dual of the group algebra of a compact group’, J. London Math. Soc. 35 (1987), 135–148.CrossRefGoogle Scholar
[9] Lau, A. T. and Pym, J., ‘Concerning the second dual of the group algebra of a locally compact group’, J. London Math. Soc. 41 (1990), 445–460.CrossRefGoogle Scholar
[10] Lau, A. T. and Ülger, A., ‘Topological centers of certain dual algebras’, Trans. Amer. Math. Soc. 348 (1996), 1191–1212.CrossRefGoogle Scholar
[11] Losert, V., ‘Weakly compact multipliers on group algebras’, J. Funct. Anal. 213 (2004), 466–472.CrossRefGoogle Scholar
[12] Mehdipour, M. J. and Nasr-Isfahani, R., ‘Completely continuous elements of Banach algebras related to locally compact groups’, Bull. Austral. Math. Soc. 76 (2007), 49–54.CrossRefGoogle Scholar
[13] Sakai, S., ‘Weakly compact operators on operator algebras’, Pacific J. Math. 14 (1964), 659–664.CrossRefGoogle Scholar