Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-13T10:14:56.224Z Has data issue: false hasContentIssue false
  • English
  • Français

Multipliers of Banach valued function spaces

Part of: Abstract harmonic analysis Permutation groups Normed linear spaces and Banach spaces; Banach lattices Measures, integration, derivative, holomorphy

Published online by Cambridge University Press:  09 April 2009

Hang-Chin Lai
Hang-Chin Lai
Affiliation:
Institute of Mathematics National Tsing Hua UniversityTaiwan, Republic of China
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.

Let A be a commutative Banach algebra with identity of norm 1, X a Banach A-module and G a locally compact abeian group with Haar measure. Then the multipliers from an A -valued function algebra into an X-valued function space is studied. We characterize the multiplier spaces as the following isometrically isomorphic relations under some appropriate conditions:

Keywords

Banach modulehomomorphisminvariant operatormultiplierBochner integralvector measure.

MSC classification

Secondary: 20B05: General theory for finite groups 43A22: Homomorphisms and multipliers of function spaces on groups, semigroups, etc. 46G10: Vector-valued measures and integration 46B22: Radon-Nikodým, Kreĭn-Milman and related properties
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 39 , Issue 1 , August 1985 , pp. 51 - 62
Copyright
Copyright © Australian Mathematical Society 1985

References

[1]Dinculeanu, N., Vector measures (Pergamon, Oxford, 1967).CrossRefGoogle Scholar
[2]Dinculeanu, N., Integration on locally compact spaces (Math. Surveys, Amer. Math. Soc., No. 15, 1974).Google Scholar
[3]Diestel, J. and Uhl, J. J. Jr, Vector measures (Math. Surveys, Amer. Math. Soc., No. 15, 1977).CrossRefGoogle Scholar
[4]Graven, A. W. M., ‘Tensor products and multipliers of L 1(G)-modules’, Indag. Math. 38 (1976), 313–325.CrossRefGoogle Scholar
[5]Hewitt, E., ‘The ranges of certain convolution operators’, Math. Scand. 15 (1964), 147–155.CrossRefGoogle Scholar
[6]Johnson, G. P., ‘Spaces of functions with values in a Banach algebra’, Trans. Amer. Math. Soc. 92 (1959), 411–429.CrossRefGoogle Scholar
[7]Lai, H. C., ‘Duality of Banach function spaces and the Radon Nikodym property’, preprint.Google Scholar
[8]Lai, H. C., ‘Multipliers of a Banach algebra in the second conjugate algebra as an idealizer’, Tôhoku Math. J. 26 (1974), 431–452.CrossRefGoogle Scholar
[9]Lai, H. C. and Chen, I. S., ‘Harmonic analysis on the Fourier algebras A 1,p (G)’, J. Austral. Math. Soc. (Series A) 30 (1981), 438–452.CrossRefGoogle Scholar
[10]Larsen, R., An introduction to the theory of multipliers (Springer-Verlag, Berlin and New York, 1971).CrossRefGoogle Scholar
[11]Rieffel, M., ‘Multipliers and tensor products of Lp-spaces of locally compact groups’, Studia Math. 33 (1969), 71–82.CrossRefGoogle Scholar
[12]Rieffel, M., ‘Induced Banach representations of Banach algebras and locally compact groups’, J. Functional Analysis 1 (1967), 443–491.CrossRefGoogle Scholar
[13]Tewari, U. B., Dutta, M. and Vaidya, D. P., ‘Multipliers of group algebra of vector-valued functions’, Proc. Amer. Math. Soc. 81 (1981), 223–229.CrossRefGoogle Scholar
[14]Thomas, E., The Lebesgue-Nikodym theorem for vector valued Radon measures (Memoirs of Amer. Math. Soc. No. 139, 1974).CrossRefGoogle Scholar