Invariant subspaces for polynomially hyponormal operators

Prunaru, Bebe

doi:10.1090/S0002-9939-97-03980-4

Invariant subspaces for polynomially hyponormal operators
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Proc. Amer. Math. Soc. 125 (1997), 1689-1691 Request permission

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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