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

• Autorzy: W. Żelazko
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47A67: Representation theory
• 16G30: Representations of orders, lattices, algebras over commutative rings

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1998
• Tom: 130
• Numer: 3
• Strony: 293-296

Daty

wydano

1998

otrzymano

1998-02-03

poprawiono

1998-03-24

Twórcy

autor

W. Żelazko

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

Bibliografia

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