- PARANORMAL CONTRACTIONS AND INVARIANT SUBSPACES
- Duggal, B.P. ; Kubrusly, C.S. ; Levan, N. ;
- Journal of the Korean Mathematical Society, volume 40, issue 6, 2003, Pages 933~942
- DOI : 10.4134/JKMS.2003.40.6.933

Abstract

It is shown that if a paranormal contraction T has no nontrivial invariant subspace, then it is a proper contraction. Moreover, the nonnegative operator Q = T/sup 2*/T/sup 2/ - 2T/sup */T ＋ I also is a proper contraction. If a quasihyponormal contraction has no nontrivial invariant subspace then, in addition, its defect operator D is a proper contraction and its itself-commutator is a trace-class strict contraction. Furthermore, if one of Q or D is compact, then so is the other, and Q and D are strict ontraction.