Journal of Operator Theory

Volume 38, Issue 2, Fall 1997 pp. 323-328.

Equivalent invariant subspace problems

Authors: Carlos S. Kubrusly
Author institution:Catholic University - PUC/RJ; and National Laboratory for Scientific Computation - LNCC, 22290-160, Rio de Janeiro, BRAZIL

Summary: An elementary proof for the equivalence of two open questions for Hilbert-space operators is established: every contraction that does not belong to the class $\mathcal C_{00}$ has a nontrivial invariant subspace if and only if every contraction which is a quasiaffine transform of a unitary operator has a nontrivial invariant subspace.

Keywords: Hilbert-space operators, invariant subspaces, C_{00}-contractions, quasiaffine transforms.

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