Invariant subspaces for polynomially hyponormal operators

Prunaru, Bebe

doi:10.1090/s0002-9939-97-03980-4

Proc. Amer. Math. Soc.

1997

DOI: 10.1090/s0002-9939-97-03980-4

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Invariant subspaces for polynomially hyponormal operators

Bebe Prunaru

Abstract: Abstract. We show that if T is a bounded operator on a Hilbert space such that p(T ) * p(T )−p(T )p(T ) * ≥ 0 for every polynomial p, then T has a nontrivial invariant subspace.

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An operator-theoretic approach to truncated moment problems

Curto

1997

Banach Center Publ.

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We survey recent developments in operator theory and moment problems, beginning with the study of quadratic hyponormality for unilateral weighted shifts, its connections with truncated Hamburger, Stieltjes, Hausdorff and Toeplitz moment problems, and the subsequent proof that polynomially hyponormal operators need not be subnormal. We present a general elementary approach to truncated moment problems in one or several real or complex variables, based on matrix positivity and extension. Together with the construction of a "functional calculus" for the columns of the associated moment matrix, our operator-theoretic approach allows us to obtain existence theorems for the truncated complex moment problem, in case the columns satisfy one of several natural constraints. We also include an application to the Riemann-quadrature problem from numerical analysis.

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An operator-theoretic approach to truncated moment problems

Curto

1997

Banach Center Publ.

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Invariant subspaces for polynomially hyponormal operators

Abstract: Abstract. We show that if T is a bounded operator on a Hilbert space such that p(T ) * p(T )−p(T )p(T ) * ≥ 0 for every polynomial p, then T has a nontrivial invariant subspace.

Cited by 1 publication

References 11 publications

An operator-theoretic approach to truncated moment problems

An operator-theoretic approach to truncated moment problems

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