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GENERALIZED WEYL’S THEOREM FOR FUNCTIONS OF OPERATORS AND COMPACT PERTURBATIONS

Ting Ting Zhou|Chun Guang Li|Sen Zhu
대한수학회 (The Korean Mathematical Society)|2012.09|대한수학회보 (Bulletin of the KMS)|제49권 제5호|pp. 899-910

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참고문헌

키워드

generalized Weyl's theoremoperator approximationcompact perturbations
주제분류수학

초록

Let $\mathcal{H}$ be a complex separable infinite dimensional Hilbert space. In this paper, a necessary and sufficient condition is given for an operator T on $\mathcal{H}$ to satisfy that $f(T)$ obeys generalized Weyl's theorem for each function $f$ analytic on some neighborhood of ${\sigma}(T)$. Also we investigate the stability of generalized Weyl's theorem under (small) compact perturbations.

Abstract

Let $\mathcal{H}$ be a complex separable infinite dimensional Hilbert space. In this paper, a necessary and sufficient condition is given for an operator T on $\mathcal{H}$ to satisfy that $f(T)$ obeys generalized Weyl's theorem for each function $f$ analytic on some neighborhood of ${\sigma}(T)$. Also we investigate the stability of generalized Weyl's theorem under (small) compact perturbations.

참고문헌 (26)

  1. P. Aiena, "Property (w) and perturbations. II", J. Math. Anal. Appl, 42(2), pp.830~837 (2008)
  2. P. Aiena, "Generalized Weyl’s theorem and quasi-affinity", Studia Math, 198(2), pp.105~120 (2010)
  3. P. Aiena, "Property (w) and perturbations", J. Math. Anal. Appl, 336(1), pp.683~692 (2007)
  4. P. Aiena, "Property (w) and perturbations. III", J. Math. Anal. Appl, 353(1), pp.205~214 (2009)
  5. M. Amouch, "Weyl type theorems for operators satisfying the single-valued extension property", J. Math. Anal. Appl, 326(2), pp.1476~1484 (2007)
  6. I. J. An, "Weyl’s theorem for algebraically quasi-class A operators", Integral Equations Operator Theory, 62(1), pp.1~10 (2008)
  7. S. K. Berberian, "An extension of Weyl’s theorem to a class of not necessarily normal operators", Michigan Math. J, 16, pp.273~279 (1969)
  8. M. Berkani, "Index of B-Fredholm operators and generalization of a Weyl theorem", Proc. Amer. Math. Soc, 130(6), pp.1717~1723 (2002)
  9. M. Berkani, "On the equivalence of Weyl theorem and generalized Weyl theorem", Acta Math. Sin. (Engl. Ser.), 23(1), pp.103~110 (2007)
  10. M. Berkani, "Generalized Weyl’s theorem and hyponormal operators", J. Aust. Math. Soc, 76(2), pp.291~302 (2004)
  11. M. Berkani, "Weyl type theorems for bounded linear operators", Acta Sci. Math, 69(1), pp.359~376 (2003)
  12. M. Berkani, "On semi B-Fredholm operators", Glasg. Math. J, 43(3), pp.457~465 (2001)
  13. X. H. Cao, "Topological uniform descent and Weyl type theorem", Linear Algebra Appl, 420(1), pp.175~182 (2007)
  14. X. H. Cao, "Weyl type theorems for p-hyponormal and M- hyponormal operators", Studia Math, 163(2), pp.177~188 (2004)
  15. L. A. Coburn, "Weyl’s theorem for nonnormal operators", Michigan Math. J, 13, pp.285~288 (1966)
  16. J. B. Conway, "A course in Functional Analysis, second ed.", Graduate Texts in Mathematics, 96 (1990), Springer-Verlag
  17. R. E. Curto, "Generalized Browder’s and Weyl’s theorems for Banach space operators", J. Math. Anal. Appl, 336(2), pp.1424~1442 (2007)
  18. B. P. Duggal, "Hereditarily polaroid operators, SVEP and Weyl’s theorem", J. Math. Anal. Appl, 340(1), pp.366~373 (2008)
  19. N. Dunford, "Linear Operators. Part I" (1988), A Wiley-Interscience Publication, John Wiley & Sons, Inc.
  20. D. A. Herrero, "Economical compact perturbations. II. Filling in the holes", J. Operator Theory, 19(1), pp.25~42 (1988)
  21. D. A. Herrero, "Approximation of Hilbert Space Operators. Vol. 1, second ed., In Pitman Research Notes in Mathematics Series, vol. 224" (1989), Longman Scientific & Technical
  22. C. G. Li, "Weyl’s theorem for functions of operators and ap- proximation", Integral Equations Operator Theory, 67(4), pp.481~497 (2010)
  23. H. Radjavi, "Invariant Subspaces, second ed." (2003), Dover Publications Inc.
  24. H. Weyl, "Uber beschrankte quadratische formen, deren differenz, vollsteig ist", Rend. Circ. Mat. Palermo, 27, pp.373~392 (1909)
  25. H. Zguitti, "A note on generalized Weyl’s theorem", J. Math. Anal. Appl, 316(1), pp.373~381 (2006)
  26. S. Zhu, "SVEP and compact perturbations", J. Math. Anal. Appl, 380(1), pp.69~75 (2011)

관련 논문AI추천

A NOTE ON WEYL’S THEOREM FOR -PARANORMAL OPERATORS김안현대한수학회 · 대한수학회논문집2012 · 제27권 제3호The spectral continuity of essentially hyponormal operators김안현, 류은진대한수학회 · 대한수학회논문집2014 · 제29권 제3호WEYL’S THEOREM AND TENSOR PRODUCT FOR OPERATORS SATISFYING T *k|T 2|T k≥T *k|T |2T k김인현대한수학회 · 대한수학회지2010 · 제47권 제2호Weyl Type Theorems for Unbounded Hyponormal OperatorsAnuradha Gupta, Karuna Mamtani경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2015 · 제55권 제3호Continuity of spectra and compact perturbationsSalvador Sanchez-Perales, Slavisa V. Djordjevic대한수학회 · 대한수학회보2011 · 제48권 제6호GENERALIZED BROWDER, WEYL SPECTRA AND THE POLAROID PROPERTY UNDER COMPACT PERTURBATIONS김인현, Bhaggy P. Duggal대한수학회 · 대한수학회지2017 · 제54권 제1호

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