대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제42권1호
  • /
  • Pages.169-177
  • /
  • 2005
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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CONTRACTIONS OF CLASS Q AND INVARIANT SUBSPACES

  • DUGGAL, B.P. (5 Tudor Court, Amherst Road, London W13 8NE, England) ;
  • KUBRUSLY, C.S. (Catholic University of Rio de Janeiro) ;
  • LEVAN, N. (University of California Los Angeles, Los Angeles)
  • 발행 : 2005.02.01
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초록

A Hilbert Space operator T is of class Q if $T^2{\ast}T^2-2T{\ast}T + I$ 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 = $T^2{\ast}T^2-2T{\ast}T + I$ also is a proper contraction.

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참고문헌

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  3. A note on roots and powers of partial isometries vol.110, pp.3, 2018, https://doi.org/10.1007/s00013-017-1116-2
  4. Operators satisfying a similarity condition pp.1563-5139, 2019, https://doi.org/10.1080/03081087.2018.1435625