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An extension of Burnside’s Theorem to infinite-dimensional spaces

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Abstract

The classical Burnside’s Theorem guarantees in a finite dimensional space the existence of invariant subspaces for a proper subalgebra of the matrix algebra. In this paper we give an extension of Burnside’s Theorem for a general Banach space, which also gives new results on invariant subspaces.

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Authors and Affiliations

  1. Department of Mathematics, Kent State University, 44242, Kent, OH, USA

    V. Lomonosov

Authors
  1. V. Lomonosov
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Partially supported by a grant from the National Science Foundation.

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Lomonosov, V. An extension of Burnside’s Theorem to infinite-dimensional spaces. Israel J. Math. 75, 329–339 (1991). https://doi.org/10.1007/BF02776031

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  • DOI: https://doi.org/10.1007/BF02776031

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