Israel Journal of Mathematics

, Volume 75, Issue 2–3, pp 329–339 | Cite as

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

  • V. Lomonosov


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.


Banach Space Compact Operator General Banach Space Finite Multiplicity Proper Subalgebra 
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Copyright information

© Hebrew University 1991

Authors and Affiliations

  • V. Lomonosov
    • 1
  1. 1.Department of MathematicsKent State UniversityKentUSA

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