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A note on multipliers of Lp(G, A)

Published online by Cambridge University Press:  09 April 2009

Serap Öztop
Affiliation:
Istanbul UniversityFaculty of Sciences Department of Mathematics 34459 Vezneciler/IstanbulTurkey e-mail: serapoztop@hotmail.com, oztops@istanbul.edu.tr
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Abstract

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Let G be a locally compact abelian group, 1 < p < ∞, and A be a commutative Banach algebra. In this paper we study the space of multipliers on Lp (G, A) and characterize it as the space of multipliers of certain banach algebra. We also study the multipliers space on L1 (G, A) ∩ Lp (G, A).

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2003

References

[1]Datry, C., Multiplicateurs d'un L1(G)-module de Banach consideres comme multiplicateurs d'une certaine algèbre de Banach (Groupe de travail d'Analyse Harmonique, Institut Fourier, Grenoble, 1981).Google Scholar
[2]Dinculeanu, N., Integration on locally compact spaces, (Nordhoff, The Netherlands, 1974).Google Scholar
[3]Feichtinger, H., ‘Multipliers of Banach spaces of functions on groups’, Math. Z. 152 (1976), 4758.CrossRefGoogle Scholar
[4]Fisher, M. J., ‘Properties of three algebras related to Lp-multipliers’, Bull. Amer. Math. Soc. 80 (1974), 262265.CrossRefGoogle Scholar
[5]Griffin, J. and McKennon, K., ‘Multipliers and group Lp algebras’, Pacific J. Math. 49 (1973), 365370.Google Scholar
[6]Johnson, G. P., ‘Spaces of functions with values in a Banach algebra’, Trans. Amer. Math. Soc. 92 (1959), 411429.Google Scholar
[7]Lai, H. C., ‘Multipliers of Banach-valued function spaces’, J. Austral. Math. Soc. (Ser. A) 39 (1985), 5162.Google Scholar
[8]Lai, H. C. and Chang, T. K., ‘Multipliers and translation invariant operators’, Tohoku Math. J. 41 (1989), 3141.CrossRefGoogle Scholar
[9]Larsen, R., An introduction to the theory of multipliers (Springer, Berlin, 1971).Google Scholar
[10]McKennon, K., ‘Multipliers of type (p, p)’, Pacific J. Math. 43 (1972), 429436.CrossRefGoogle Scholar
[11]McKennon, K., ‘Multipliers of type (p, p) and multipliers of group Lp algebras’, Pacific J. Math. 45 (1972), 297302.CrossRefGoogle Scholar
[12]McKennon, K., ‘Corrections to [10, 11] and [5]’, Pacific J. Math. 61 (1975), 603606.CrossRefGoogle Scholar
[13]Rieffel, M., ‘Induced Banach representations of Banach algebras and locally compact groups’, J. Funct. Anal. 1 (1967), 443491.Google Scholar
[14]Tewari, U. B., Dutta, M. and Vaidya, D. P., ‘Multipliers of group algebra of vector-valued functions’, Proc. Amer. Math. Soc. 81 (1981), 223229.CrossRefGoogle Scholar
[15]Wang, J. K., ‘Multipliers of commutative Banach algebras’, Pacific J. Math. 11 (1961), 11311149.CrossRefGoogle Scholar