# Characterization of strict C*-algebras

Studia Mathematica (1994)

- Volume: 112, Issue: 1, page 51-58
- ISSN: 0039-3223

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topAristov, O.. "Characterization of strict C*-algebras." Studia Mathematica 112.1 (1994): 51-58. <http://eudml.org/doc/216136>.

@article{Aristov1994,

abstract = {A Banach algebra A is called strict if the product morphism is continuous with respect to the weak norm in A ⊗ A. The following result is proved: A C*-algebra is strict if and only if all its irreducible representations are finite-dimensional and their dimensions are bounded.},

author = {Aristov, O.},

journal = {Studia Mathematica},

keywords = {strict -algebras; product morphism},

language = {eng},

number = {1},

pages = {51-58},

title = {Characterization of strict C*-algebras},

url = {http://eudml.org/doc/216136},

volume = {112},

year = {1994},

}

TY - JOUR

AU - Aristov, O.

TI - Characterization of strict C*-algebras

JO - Studia Mathematica

PY - 1994

VL - 112

IS - 1

SP - 51

EP - 58

AB - A Banach algebra A is called strict if the product morphism is continuous with respect to the weak norm in A ⊗ A. The following result is proved: A C*-algebra is strict if and only if all its irreducible representations are finite-dimensional and their dimensions are bounded.

LA - eng

KW - strict -algebras; product morphism

UR - http://eudml.org/doc/216136

ER -

## References

top- [1] J. Dixmier, Les C*-algèbres et leurs représentations, Gauthier-Villars, Paris, 1964.
- [2] A. Grothendieck, Produits tensorielles et espaces nucléaires, Mem. Amer. Math. Soc. 166 (1955).
- [3] A. Ya. Helemskiĭ, Banach and Locally Convex Algebras, Clarendon Press, Oxford, 1993.
- [4] R. V. Kadison, Irreducible operator algebras, Proc. Nat. Acad. Sci. U.S.A. 43 (1957), 273-276. Zbl0078.11502
- [5] E. Sh. Kurmakaeva, On the strictness of algebras and modules, preprint, Moscow University, No. 1548-B92, VINITI, 1992 (in Russian).
- [6] N. Th. Varopoulos, Some remarks on Q-algebras, Ann. Inst. Fourier (Grenoble) 22 (4) (1972), 1-11. Zbl0235.46074

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