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

W. Żelazko

Studia Mathematica (1998)

  • Volume: 130, Issue: 3, page 293-296
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Żelazko, W.. "A density theorem for algebra representations on the space (s)." Studia Mathematica 130.3 (1998): 293-296. <http://eudml.org/doc/216559>.

@article{Żelazko1998,
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.},
author = {Żelazko, W.},
journal = {Studia Mathematica},
keywords = {irreducible representations; locally convex spaces; totally irreducible; strong operator topology; commutant; Jacobson density theorem; topology of coordinatewise convergence; infinite topological product of the field of scalars},
language = {eng},
number = {3},
pages = {293-296},
title = {A density theorem for algebra representations on the space (s)},
url = {http://eudml.org/doc/216559},
volume = {130},
year = {1998},
}

TY - JOUR
AU - Żelazko, W.
TI - A density theorem for algebra representations on the space (s)
JO - Studia Mathematica
PY - 1998
VL - 130
IS - 3
SP - 293
EP - 296
AB - 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.
LA - eng
KW - irreducible representations; locally convex spaces; totally irreducible; strong operator topology; commutant; Jacobson density theorem; topology of coordinatewise convergence; infinite topological product of the field of scalars
UR - http://eudml.org/doc/216559
ER -

References

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  1. [1] S. Banach, Théorie des Opérations Linéaires, Warszawa, 1932. Zbl0005.20901
  2. [2] F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer, 1973. Zbl0271.46039
  3. [3] J. M. G. Fell and R. S. Doran, Representations of *-Algebras, Locally Compact Groups, and Banach *-Algebraic Bundles, Vol. I, Academic Press, 1988. Zbl0652.46050
  4. [4] N. Jacobson, Lectures in Abstract Algebra, Vol. II, van Nostrand, 1953. 
  5. [5] G. Köthe, Topological Vector Spaces I, Springer, 1969. 
  6. [6] S. Rolewicz, Metric Linear Spaces, PWN and Reidel, 1984. 
  7. [7] H. H. Schaefer, Topological Vector Spaces, Springer, 1971. 
  8. [8] W. Żelazko, A density theorem for F-spaces, Studia Math. 96 (1990), 159-166. Zbl0745.46010
  9. [9] W. Żelazko, On a problem of Fell and Doran, Colloq. Math. 62 (1991), 31-37. Zbl0765.46031

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