Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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PARANORMAL CONTRACTIONS AND INVARIANT SUBSPACES

  • Duggal, B.P. (United Arab Emirates University) ;
  • Kubrusly, C.S. (Catholic University of Rio de Janeiro) ;
  • Levan, N. (University of California in Los Angeles)
  • Published : 2003.11.01
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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.

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