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

Studia Mathematica (1998)

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

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topŻelazko, 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

top- [1] S. Banach, Théorie des Opérations Linéaires, Warszawa, 1932. Zbl0005.20901
- [2] F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer, 1973. Zbl0271.46039
- [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] 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. Zbl0745.46010
- [9] W. Żelazko, On a problem of Fell and Doran, Colloq. Math. 62 (1991), 31-37. Zbl0765.46031

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