Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Tensor products of locally convex modules and applications to the multiplier problem


Author: Roger Rigelhof
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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] N. Bourbaki, Livre V: Espace vectoriels topologique, Chaps. 1-5, Actualités Sci. Indust., no. 1189, Hermann, Paris, 1966. MR 34 #3277.
  • [2] -, 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.
  • [3] B. Brainerd and R. E. Edwards, Linear operators which commute with translations. I: Representation theorems, J. Austral. Math. Soc. 6 (1966), 289-327. MR 34 #6542. MR 0206725 (34:6542)
  • [4] G. Gaudry, Quasimeasures and operators commuting with convolution, Pacific J. Math. 18 (1966), 461-476. MR 34 #3352. MR 0203502 (34:3352)
  • [5] R. Larsen, The multiplier problem, Lecture Notes in Math., No. 105, Springer-Verlag, Berlin, 1969. MR 0435737 (55:8694)
  • [6] L. Máté, The Arens product and multiplier operators, Studia Math. 28 (1966/67), 227-234. MR 35 #5938. MR 0215095 (35:5938)
  • [7] M. A. Rieffel, Induced Banach representations of Banach algebras and locally compact groups, J. Functional Analysis 1 (1967), 443-491. MR 36 #6544. MR 0223496 (36:6544)
  • [8] -, Multipliers and tensor products of $ {L^p}$-spaces of locally compact groups, Studia Math. 33 (1969), 71-82. MR 39 #6078. MR 0244764 (39:6078)
  • [9] R. Rigelhof, Induced representations of locally compact groups, Acta Math. 125 (1970), 155-188. MR 0281836 (43:7550)
  • [10] W. Rudin, Fourier analysis on groups, Interscience Tracts in Pure and Appl. Math., no. 12, Interscience, New York, 1962. MR 27 #2808. MR 0152834 (27:2808)
  • [11] H. H. Schaefer, Topological vector spaces, Macmillan, New York, 1966. MR 33 #1689. MR 0193469 (33:1689)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 43A22, 46M05

Retrieve articles in all journals with MSC: 43A22, 46M05


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1972-0293335-4
Keywords: Locally convex modules, tensor products, locally convex algebras, Banach modules, multipliers
Article copyright: © Copyright 1972 American Mathematical Society

American Mathematical Society