Tensor products of locally convex modules and applications to the multiplier problem
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- by Roger Rigelhof PDF
- Trans. Amer. Math. Soc. 164 (1972), 295-307 Request permission
Abstract:
In this paper we present a representation theorem for the tensor product of locally convex modules. This theorem has a number of consequences in the study of the multiplier problem in harmonic analysis, and the remainder of the paper is devoted to these applications.References
-
N. Bourbaki, Livre V: Espace vectoriels topologique, Chaps. 1-5, Actualités Sci. Indust., no. 1189, Hermann, Paris, 1966. MR 34 #3277.
—, Livre VI: Intégration, Chaps. 1-8, Actualités Sci. Indust., nos. 1175, 1244, 1306, Hermann, Paris, 1965, 1967, 1963. MR 36 #2763; MR 35 #322; MR 31 #3539.
- B. Brainerd and R. E. Edwards, Linear operators which commute with translations. I. Representation theorems, J. Austral. Math. Soc. 6 (1966), 289–327. MR 0206725, DOI 10.1017/S1446788700004286
- G. I. Gaudry, Quasimeasures and operators commuting with convolution, Pacific J. Math. 18 (1966), 461–476. MR 203502, DOI 10.2140/pjm.1966.18.461
- Ronald Larsen, The multiplier problem, Lecture Notes in Mathematics, Vol. 105, Springer-Verlag, Berlin-New York, 1969. MR 0435737, DOI 10.1007/BFb0059711
- L. Máté, The Arens product and multiplier operators, Studia Math. 28 (1966/67), 227–234. MR 215095, DOI 10.4064/sm-28-3-227-234
- Marc A. Rieffel, Induced Banach representations of Banach algebras and locally compact groups, J. Functional Analysis 1 (1967), 443–491. MR 0223496, DOI 10.1016/0022-1236(67)90012-2
- Marc A. Rieffel, Multipliers and tensor products of $L^{p}$-spaces of locally compact groups, Studia Math. 33 (1969), 71–82. MR 244764, DOI 10.4064/sm-33-1-71-82
- Roger Rigelhof, Induced representations of locally compact groups, Acta Math. 125 (1970), 155–187. MR 281836, DOI 10.1007/BF02392333
- Walter Rudin, Fourier analysis on groups, Interscience Tracts in Pure and Applied Mathematics, No. 12, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0152834
- Helmut H. Schaefer, Topological vector spaces, The Macmillan Company, New York; Collier Macmillan Ltd., London, 1966. MR 0193469
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 164 (1972), 295-307
- MSC: Primary 43A22; Secondary 46M05
- DOI: https://doi.org/10.1090/S0002-9947-1972-0293335-4
- MathSciNet review: 0293335