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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Reductive algebras of compact operators


Author: Robert A. Bekes
Journal: Proc. Amer. Math. Soc. 48 (1975), 365-370
DOI: https://doi.org/10.1090/S0002-9939-1975-0358381-9
MathSciNet review: 0358381
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Abstract: A closed subalgebra $\mathfrak {A}$ of the bounded operators on a Hilbert space is called reductive if every closed invariant subspace for $\mathfrak {A}$ is reducing for $\mathfrak {A}$. We show that every reductive subalgebra of the compact operators is selfadjoint.


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Keywords: Algebra of operators, compact operators, invariant subspace, reducing subspaces, selfadjoint algebra
Article copyright: © Copyright 1975 American Mathematical Society