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Contractions of Class Q and Invariant Subspaces

B. P. Duggal|C. S. Kubrusly|N. Levan
대한수학회 (The Korean Mathematical Society)|2005.02|대한수학회보 (Bulletin of the KMS)|제42권 제1호|pp. 169-177

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Abstract

A Hilbert Space operator T is of class Q ifT^{2*}T^2-2kern1ptT^*T+I is nonnegative. Every paranormaloperator is of class Q, but class-Q operators are notnecessarily normaloid. It is shown that if a class-Qcontraction T has no nontrivial invariant subspace, then it is aproper contraction. Moreover, the nonnegative operatorQ=T^{2*}T^2-2kern1ptT^*T+I also is a propercontraction.

참고문헌 (9)

  1. T. And, "Operators with a norm condition", 1972, pp.szeged, 169~
  2. N. N. Chourasia, "Paranormal operators onBanach spaces", 1980, pp.21, 161~
  3. B. P. Duggal, "Generalized Weyl'stheorem for a class of operators satisfying a norm condition", 2004, pp.104, 75~81
  4. B. P. Duggal, 6I. H. Jeon,, "Contractionssatisfying the absolute value property", 2004, pp.49, 141~
  5. B. P. Duggal,C. S. Kubrusly, "Paranormalcontractions and invariant subspaces", ,, 2003, pp.j40, 933~942
  6. T. Furuta., "Invitation to Linear Operators", 2001., ~
  7. "Hilbert Space Operators", 2003., ~
  8. "Proper contractions andinvariant subspaces", 2001, pp.28, 223~230
  9. "Paranormal operators with countable spectrum are normal operators", 1987, pp.7, 591~

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