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A lemma on the approximation of finite-dimensional*-algebras

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Abstract

One proves an analog of Glimm's lemma [Trans. Am. Math. Soc.,95, No. 2, 318–340 (1960)] by replacing the uniform norm by the trace norm ∥A∥=tr(AA*)1/2; if the elements of a finite type factor satisfy (up to δ) the relations which have to be satisfied by the matrix units of a finite-dimensional*-algebraA, then in theirε -neighborhoods there exist operators which satisfy exactly these relations and δ depends only on the algebraic type ofA and ofε.

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Literature cited

  1. J. G. Glimm, Trans. Am. Math. Soc.,95., No. 2, 318–340 (1960).

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  2. J. Dixmier, Les Algebres d'Operateurs dans l'Espace Hilbertien, Gauthier-Villars, Paris (1957).

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  3. P. R. Halmos, Trans. Am. Math. Soc.,144, 381–389 (1969).

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Authors
  1. A. A. Lodkin
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 47, pp. 175–178, 1974.

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Lodkin, A.A. A lemma on the approximation of finite-dimensional*-algebras. J Math Sci 9, 280–283 (1978). https://doi.org/10.1007/BF01578554

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  • DOI: https://doi.org/10.1007/BF01578554

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