A density theorem for algebra representations on the space (s)

W. Żelazko

ArticleOriginal scientific text

Title

A density theorem for algebra representations on the space (s)

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Affiliations

Institute of Mathematics Polish Academy of Sciences, P.O. Box 137, Śniadeckich 8, 00-950 Warszawa, Poland

Abstract

We show that an arbitrary irreducible representation T of a real or complex algebra on the F-space (s), or, more generally, on an arbitrary infinite (topological) product of the field of scalars, is totally irreducible, provided its commutant is trivial. This provides an affirmative solution to a problem of Fell and Doran for representations on these spaces.

S. Banach, Théorie des Opérations Linéaires, Warszawa, 1932.
F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer, 1973.
J. M. G. Fell and R. S. Doran, Representations of *-Algebras, Locally Compact Groups, and Banach *-Algebraic Bundles, Vol. I, Academic Press, 1988.
N. Jacobson, Lectures in Abstract Algebra, Vol. II, van Nostrand, 1953.
G. Köthe, Topological Vector Spaces I, Springer, 1969.
S. Rolewicz, Metric Linear Spaces, PWN and Reidel, 1984.
H. H. Schaefer, Topological Vector Spaces, Springer, 1971.
W. Żelazko, A density theorem for F-spaces, Studia Math. 96 (1990), 159-166.
W. Żelazko, On a problem of Fell and Doran, Colloq. Math. 62 (1991), 31-37.

Title

A density theorem for algebra representations on the space (s)

Affiliations

Abstract

Bibliography