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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.
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참고문헌 (26)
참고문헌 신청
B. P. Duggal / 2008 / Hereditarily polaroid operators, SVEP and Weyl’s theorem / J. Math. Anal. Appl 340 (1) : 366 ~ 373
C. G. Li / 2010 / Weyl’s theorem for functions of operators and ap- proximation / Integral Equations Operator Theory 67 (4) : 481 ~ 497
D. A. Herrero / 1988 / Economical compact perturbations. II. Filling in the holes / J. Operator Theory 19 (1) : 25 ~ 42
D. A. Herrero / 1989 / Approximation of Hilbert Space Operators. Vol. 1, second ed., In Pitman Research Notes in Mathematics Series, vol. 224 / Longman Scientific & Technical
H. Radjavi / 2003 / Invariant Subspaces, second ed. / Dover Publications Inc.
C. G. Li / 2010 / Weyl’s theorem for functions of operators and ap- proximation / Integral Equations Operator Theory 67 (4) : 481 ~ 497
D. A. Herrero / 1988 / Economical compact perturbations. II. Filling in the holes / J. Operator Theory 19 (1) : 25 ~ 42
D. A. Herrero / 1989 / Approximation of Hilbert Space Operators. Vol. 1, second ed., In Pitman Research Notes in Mathematics Series, vol. 224 / Longman Scientific & Technical
H. Radjavi / 2003 / Invariant Subspaces, second ed. / Dover Publications Inc.
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