DOI QR코드

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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

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

  1. T. Ando, Operators with a norm condition, Acta Sci. Math. (Szeged) 33 (1972), 169-178
  2. N. N. Chourasia and P. B. Ramanujan, Paranormal operators on Banach spaces, Bull. Austral. Math. Soc. 21 (1980), 161-168 https://doi.org/10.1017/S0004972700005980
  3. B. P. Duggal and S. V. Djordjevic, Generalized Weyl's theorem for a class of operators satisfying a norm condition, Math. Proc. R. Ir. Acad. 104 (2004), 75-81 (corrigendum submitted)
  4. B. P. Duggal, S. V. Djordjevic, and C. S. Kubrusly, Hereditarily normaloid contractions, Acta Sci. Math. (Szeged), in press
  5. B. P. Duggal, I. H. Jeon, and C. S. Kubrusly, Contractions satisfying the absolute value property $IAI^2{\leq}IA^2|$, Integral Equations Operator Theory 49 (2004), 141-148 https://doi.org/10.1007/s00020-002-1202-z
  6. B. P. Duggal, C. S. Kubrusly, and N. Levan, Paranormal contractions and invariant subspaces, J. Korean Math. Soc. 40 (2003), 933-942 https://doi.org/10.4134/JKMS.2003.40.6.933
  7. T. Furuta. Invitation to Linear Operators, Taylor and Francis, London, 2001
  8. V. Istratcscu, T. Saito and T. Yoshino, On a class of operators, Tohoku Math. J. 18 (1966), 410-413 https://doi.org/10.2748/tmj/1178243383
  9. C. S. Kubrusly, Hilbert Space Operators, Birkhauser, Boston, 2003
  10. C. S. Kubrusly and N. Levan, Proper contractions and invariant subspaces, Int. J. Math. Math. Sci. 28 (2001), 223-230 https://doi.org/10.1155/S0161171201006287
  11. C. Qiu, Paranormal operators with countable spectrum are normal operators, J. Math. Res. Exposition 7 (1987), 591-594
  12. T. Saito, Hyponormal operators and related topics, Lectures on Operator Algebras, New Orleans, 1970-1971, Lecture Notes in Math. Springer, Berlin 247 (1972), 533-664

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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