Characterization of strict C*-algebras

O. Aristov

Studia Mathematica (1994)

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

Abstract

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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.

How to cite

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Aristov, 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

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

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