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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Invariant subspaces
for polynomially hyponormal operators


Author: Bebe Prunaru
Journal: Proc. Amer. Math. Soc. 125 (1997), 1689-1691
MSC (1991): Primary 47A15, 47B20; Secondary 47D25, 47D27
MathSciNet review: 1402884
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Abstract: We show that if $T$ is a bounded operator on a Hilbert space such that $p(T)^*p(T)-p(T)p(T)^*\geq 0$ for every polynomial $p$, then $T$ has a nontrivial invariant subspace.


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Additional Information

Bebe Prunaru
Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405; Institute of Mathematics, Romanian Academy, P. O. Box 1-764, 70700 Bucharest, Romania

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03980-4
PII: S 0002-9939(97)03980-4
Keywords: Hyponormal operators, dual algebras, invariant subspaces
Received by editor(s): October 30, 1995
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1997 American Mathematical Society