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Positive Functionals and Representations of Tensor Products of Symmetric Banach Algebras

Published online by Cambridge University Press:  20 November 2018

Harvey A. Smith
Harvey A. Smith*
Affiliation:
Oakland University, Rochester, Michigan
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Except for using “algebra” rather than “ring” and “compact” rather than “bicompact”, we adopt the terminology used in (6). Every symmetric algebra, Ai, will have an identity, ei All representations will be cyclic and symmetric. Sets of functionals will carry the relative weak* topology.

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 1192 - 1202
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Gelbaum, B. R., Tensor products of Banach algebras, Can. J. Math. 11 (1959), 297–310.Google Scholar
2. Gelbaum, B. R., Note on the tensor product of Banach algebras, Proc. Amer. Math. Soc. 12 (1961), 750–757.Google Scholar
3. de Lamadrid, J. Gil, Uniform cross norms and tensor products of Banach algebras, Bull. Amer. Math. Soc. 69 (1963), 797–803.Google Scholar
4. Mackey, G. W., Induced representations of locally compact groups. II. The Frobenius reciprocity theorem, Ann. of Math. (2) 58 (1953), 193–221.Google Scholar
5. Murray, F. J. and J. von Neumann, On rings of operators. I, Ann. of Math. 37 (1936), 116–229.Google Scholar
6. Naïmark, M. A., Normed rings (P. Noordhoff, Groningen, 1959).Google Scholar
7. Schatten, R., A theory of cross-spaces, Ann. Math. Studies, No. 26 (Princeton Univ. Press, Princeton, N.J., 1950).Google Scholar
8. Schur, I., Bemerkungen zur Théorie der Beschrankten Bilinearformen mit unendlich vielen Verànderlichen, J. Math. 140 (1911), 1–28.Google Scholar
9. Smith, H. A., Tensor products of locally convex algebras, Proc. Amer. Math. Soc. 17 (1966), 124–132.Google Scholar
10. Tomiyama, J., Tensor products of commutative Banach algebras, Tohoku Math. J. 12 (1960), 147–154.Google Scholar