CONTRACTIONS OF CLASS Q AND INVARIANT SUBSPACES

Title & Authors
CONTRACTIONS OF CLASS Q AND INVARIANT SUBSPACES
DUGGAL, B.P.; KUBRUSLY, C.S.; LEVAN, N.;

Abstract
A Hilbert Space operator T is of class Q if $\small{T^2{\ast}T^2-2T{\ast}T + I}$ is nonnegative. Every paranormal operator is of class Q, but class-Q operators are not necessarily normaloid. It is shown that if a class-Q contraction T has no nontrivial invariant subspace, then it is a proper contraction. Moreover, the nonnegative operator Q = $\small{T^2{\ast}T^2-2T{\ast}T + I}$ also is a proper contraction.
Keywords
paranormal operators;invariant subspaces;proper contractions;
Language
English
Cited by
1.
Quasi-isometries in semi-Hilbertian spaces, Linear Algebra and its Applications, 2009, 430, 8-9, 2474
2.
On Wold-type decomposition, Linear Algebra and its Applications, 2012, 436, 9, 3065
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