Judgement on stability of Weyl&rsquo;s theorem for the upper triangular operator matrices

YIN Jun-Qiang; CAO Xiao-Hong

doi:10.7523/j.issn.2095-6134.2013.05.003

Journal of University of Chinese Academy of Sciences >

2013 , Vol. 30 >Issue 5: 591 - 597

DOI: https://doi.org/10.7523/j.issn.2095-6134.2013.05.003

Judgement on stability of Weyl’s theorem for the upper triangular operator matrices

YIN Jun-Qiang ,
CAO Xiao-Hong

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College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, China

Received date: 2012-07-06

Revised date: 2012-10-31

Online published: 2013-09-15

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Abstract

An operator T is said to satisfy a-Browder's theorem if σ_a(T)\σ_ea(T)???π₀₀^a(T), where σ_a(T) and σ_ea(T) denote the approximate point spectrum and the essential approximate point spectrum, respectively, and π₀₀^a(T)={λ∈isoσ_a(T),0< dimN(T-λI)<∞}. If σ_a(T)\σ_ea(T)=π₀₀^a(T), we say that T satisfies a-Weyl's theorem. In this note, by using the characteristics of semi-Fredholm domain of the diagonal of the upper triangular operator matrix, we investigate the stability of a-Browder's theorem and a-Weyl's theorem for the upper triangular operator matrices under compact perturbations.

Key words： upper triangular operator matrices; a-Browder’s theorem; compact perturbations; asymptotic intertwining operator; semi-Fredholm domain

Cite this article

YIN Jun-Qiang , CAO Xiao-Hong . Judgement on stability of Weyl’s theorem for the upper triangular operator matrices[J]. Journal of University of Chinese Academy of Sciences, 2013 , 30(5) : 591 -597 . DOI: 10.7523/j.issn.2095-6134.2013.05.003

References

[1] Weyl H. Über beschränkte quadratische Formen, deren Differenz vollstetig ist[J]. Rendiconti del Circolo Matematico di Palermo, 1909, 27: 373-392.
[2] Harte R, Lee W Y. Another note on Weyl's theorem[J]. Transactions of the American Mathematical Society, 1997, 349: 2115-2124.
[3] Rakočeviċ V. Operators obeying a-Weyl's theorem[J]. Revue Roumaine de Mathematique Pures, 1989, 34(10): 915-919.
[4] Rakočeviċ V. On a class of operators[J]. Matematicki Vesnik, 1985, 37: 423-426.
[5] Lausen K B, Neumann M M. An introduction to local spectral theory[M]. New York: Clarendon Press, 2000.
[6] Müller V. Spectral theory of linear operators[M]. Berlin:Birhkäuser Verlag AG, 2003.
[7] Ji Y Q. Quasitriangular+small compact=strongly irreducible[J]. Trans Amer Math Soc, 1999, 351(11): 4657-4673.
[8] Zhu S, Li C G. SVEP and compact perturbations[J]. J Math Anal Appl, 2011, 380(1): 69-75.
[9] Herrero D A. Approximation of Hilbert space operators:Vol 1[M]. 2nd ed. Harlow: Longman Scientific and Technical, 1989.

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