JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2016, Vol. 51 ›› Issue (8): 15-21.doi: 10.6040/j.issn.1671-9352.0.2015.530

Previous Articles     Next Articles

Weyls theorem for the cube of operator and compact perturbations

DONG Jiong, CAO Xiao-hong*   

  1. College of Mathematics and Information Science, Shaanxi Normal University, Xian 710119, Shaanxi, China
  • Received:2015-11-09 Online:2016-08-20 Published:2016-08-08

PDF (PC)

757

Abstract: An operator T∈B(H) is said to satisfy Weyls theorem if σ(T)\σw(T)=π00(T). T∈B(H) is said to have the compact perturbations of Weyls theorem if T+K satisfies Weyls theorem for all compact operators K∈B(H). In this note, a variant of the Weyl spectrum is discussed. Using the variant, we characterize the conditions for T 3 and T satisfying the compact perturbations of Weyls theorem.

Key words: Weyls theorem, compact perturbations, Weyl-Kato decomposition

CLC Number: 

  • O177.2
[1] WEYL H V.(¨overU)ber beschränkte quadratische Formen, deren differenz vollstetig ist[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] COBURN L A. Weyls theorem for nonnormal operators[J]. Michigan Mathematical Journal, 1966, 13(3):285-288.
[4] ISTRATESCU V I. On Weyls spectrum of an operator. I[J]. Revue Roumaine Des Mathematiques Pures Et Appliquees, 1972, 17:1049-1059.
[5] OBERAI K K, OBERAI K K. On the Weyl spectrum[J]. Illinois Journal of Mathematics, 1974, 18(1974):208-212.
[6] JI Y Q. Quasitriangular+small compact=strongly irreducible[J]. Transactions of the American Mathematical Society, 1999, 351(11):4657-4673.
[7] HERRERO D A. Economical compact perturbations. II. Filling in the holes.[J]. J Operator Theory, 1988(1):25-42.
[8] LI Chunguang, ZHU Sen, FENG Youling. Weyls theorem for functions of operators and approximation[J]. Integral Equations & Operator Theory, 2010, 67(4):481-497.
[9] RADJAVI H, ROSENTHAL P. Invariant subspaces[M]. 2nd ed. New York: Dover Publications, 2003.
[10] HERRERO D A. Approximation of Hilbert space operators[M]. Harlow: Longman Scientific and Technical, 1989.
[1] CUI Miao-miao, WANG Bi-yu, CAO Xiao-hong. A note on operator matrixs [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(10): 56-61.
[2] WANG Bi-yu, CAO Xiao-hong*. The perturbation for the Browder’s theorem of operator matrix#br# [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(03): 90-95.
[3] YU Wei, CAO Xiao-hong*. Topological uniform descent and the single valued extension property [J]. J4, 2013, 48(4): 10-14.
[4] ZHAO Hai-yan, CAO Xiao-hong*. The stability of the property (ω1) for the Helton class operators [J]. J4, 2013, 48(4): 15-19.
[5] SHI Wei-juan, CAO Xiao-hong*. Judgement for the stability of Weyl′s theorem [J]. J4, 2012, 47(4): 24-27.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd