An extension of Burnside’s Theorem to infinite-dimensional spaces
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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.
KeywordsBanach Space Compact Operator General Banach Space Finite Multiplicity Proper Subalgebra
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