有界线性算子的a-Weyl定理的判定

doi:10.6040/j.issn.1671-9352.0.2019.729

Abstract

Abstract: Let H be an infinite dimensional separable complex Hilbert space and B(H) be the algebra of all bounded linear operators on H. T∈B(H) satisfies the a-Weyls theorem if σ_a(T)\σ_ea(T)=π^a00(T), where σ_a(T) and σ_ea(T) denote the approximate point spectrum and essential approximate point spectrum respectively, and π^a00(T)={λ∈iso σ_a(T):0<n(T-λI)<∞}. A new judgement for the a-Weyls theorem for operators and operator functions is given. Also, the spectrum mapping theorem related to spectrum is considered.

Key words: a-Weyls theorem, approximate point spectrum, essential approximate point spectrum

CLC Number:

O177.1

FENG-GAO Hui-zi, CAO Xiao-hong. Judgement of a-Weyls theorem for bounded linear operators[J].JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(10): 88-94.

References

[1] WEYL H V. Über beschränkte quadratische formen, deren differenz vollstetigist[J]. Rendiconti Del Circolo Matematico Di Palermo, 1909, 27(1):373-392.
[2] BERBERIAN S K. An extension of Weyls theorem to a class of not necessarily normal operators[J]. Michigan Mathematical Journal, 1969, 16(3):273-279.
[3] LI Chunguang, ZHU Sen, FENG Youling, et al. Weyls theorem for functions of operators and approximation[J]. Integral Equations and Operator Theory, 2010, 67(4):481-497.
[4] CURTO R E, HAN Y M. Weyls theorem for algebraically paranormal operators[J]. Integral Equations and Operator Theory, 2003, 47(3):307-341.
[5] AN I, HAN Y. Weyls theorem for algebraically quasi-class a operators[J]. Integral Equations and Operator Theory, 2008, 62(1):1-10.
[6] SHI Weijuan, CAO Xiaohong. Weyls theorem for the square of operator and perturbations[J]. Communications in Contemporary Mathematics, 2015, 17(5):36-46.
[7] COBURN L A. Weyls theorem for nonnormal operators[J]. Michigan Mathematical Journal, 1966, 13(3):285-288.
[8] Duggal B P. The Weyl spectrum of p-hyponormal operators[J]. Integral Equations and Operator Theory, 1997, 29(2):197-201.
[9] CAO Xiaohong. Analytically class operators and Weyls theorem[J]. Journal of Mathematical Analysis and Applications, 2006, 320(2):795-803.
[10] HARTE R, LEE W Y. Another note on Weyls theorem[J]. Transactions of the American Mathematical Society, 1997, 349(5):2115-2124.
[11] RAKOCEVIC V. Operators obeying a-Weyls theorem[J]. Revue Roumaineede Math?matiques Pureset Appliquées, 1989, 34(10):915-919.
[12] DJORDJEVIC S V, HAN Y M. Browders theorems and spectral continuity[J]. Glasgow Math, 2000, 42(3):479-486.
[13] GOLDBERG S, DAMBROSIO U. Unbounded linear operators[J]. American Mathematical Monthly, 1968, 75(7):805.
[14] TAYLOR A E. Theorems on ascent, descent, nullity and defect of linear operators[J]. Mathematische Annalen, 1966, 163(1):18-49.
[15] CAO Xiaohong, GUO Maozheng, MENG Bin, et al. Weyls spectra and Weyls theorem[J]. Journal of Mathematical Analysis and Applications, 2003, 288(2):758-767.

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Judgement of a-Weyls theorem for bounded linear operators

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