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Remarks on reductive operator algebras

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Abstract

It is shown that a weakly closed operator algebra with the property that each of its invariant subspaces is reducing and which is either strictly cyclic or has only closed invariant linear manifolds, must be a von Neumann algebra.

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Authors and Affiliations

  1. University of Toronto, Toronto, Canada

    Abie Feintuch & Peter Rosenthal

  2. University of the Negev, Be'er Sheva, Israel

    Abie Feintuch & Peter Rosenthal

Authors
  1. Abie Feintuch
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  2. Peter Rosenthal
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Feintuch, A., Rosenthal, P. Remarks on reductive operator algebras. Israel J. Math. 15, 130–136 (1973). https://doi.org/10.1007/BF02764598

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  • DOI: https://doi.org/10.1007/BF02764598

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