Bulletin of the Korean Mathematical Society
( Vol.42 NO.1 / 2005 )
 Title
Contractions of Class $\mathcal Q$ and Invariant Subspaces(eng)
 Author
B. P. Duggal ,C. S. Kubrusly ,N. Levan
 MSC
47A15, 47B20
 Publication
 Page
169-177 Page
 Abstract
1. Introduction
2. Operators of class $\mathcal Q$
3. Invariant subspace theorem for contractions of class $\mathcal Q$
 Own Status
 Keyword
paranormal operators, invariant subspaces, proper contractions
 Note
 Summary
A Hilbert Space operator $T$ is of class $Q$ if
$T^{2*}T^2-2kern1ptT^*T+I$ 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
$Q=T^{2*}T^2-2kern1ptT^*T+I$ also is a proper contraction.
 Attach
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