Weyl's theorem for algebraically totally hereditarily normaloid operators

被引:3
|
作者
Duggal, BP
机构
[1] London W5 4SZ
关键词
Weyl's theorems; single valued extension property; THNoperators;
D O I
10.1016/j.jmaa.2004.11.044
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
A Banach space operator T is an element of B(X) is said to be totally hereditarily normaloid, T is an element of THN, if every part of T is normaloid and every invertible part of T has it normaloid inverse. The operator T is said to be an H(q) operator for some integer q >= 1. T is an element of H(q), if the quasi-nilpotent part H-0(T - lambda) = (T - lambda)(-q(0)) for every complex number lambda. It is proved that if T is algebraically H(q), or T is algebraically THN and X is separable, then f(T) satisfies Weyl's theorem for every function f analytic in an open neighborhood of sigma(T), and T* satisfies a-Weyl's theorem. If also T* has the single valued extension property, then f(T) satisfies a-Weyl's theorem for every analytic function f which is non-constant on the connected components of the open neighborhood of a (T) on which it is defined. (c) 2004 Elsevier Inc. All rights reserved.
引用
收藏
页码:578 / 587
页数:10
相关论文
共 50 条
  • [11] WEYL'S THEOREM FOR ALGEBRAICALLY k-QUASICLASS A OPERATORS
    Gao, Fugen
    Fang, Xiaochun
    OPUSCULA MATHEMATICA, 2012, 32 (01) : 125 - 135
  • [12] Weyl’s Theorem for Algebraically Quasi-class A Operators
    Il Ju An
    Young Min Han
    Integral Equations and Operator Theory, 2008, 62 : 1 - 10
  • [13] Generalized Weyl's theorem for algebraically quasi-paranormal operators
    An, Il Ju
    Han, Young Min
    JOURNAL OF INEQUALITIES AND APPLICATIONS, 2012,
  • [14] Generalized weyl's theorem for algebraically quasi-paranormal operators
    Il Ju An
    Young Min Han
    Journal of Inequalities and Applications, 2012
  • [15] WEYL'S THEOREM FOR ALGEBRAICALLY ABSOLUTE-(p, r)-PARANORMAL OPERATORS
    Senthilkumar, D.
    Naik, P. Maheswari
    BANACH JOURNAL OF MATHEMATICAL ANALYSIS, 2011, 5 (01): : 29 - 37
  • [16] RIESZ PROJECTION AND WEYL'S THEOREM FOR HEREDITARILY ABSOLUTE-(p,r)-PARANORMAL OPERATORS
    Senthilkumar, D.
    Prasad, T.
    BULLETIN OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2010, 2 (03): : 100 - 108
  • [17] Polaroid operators and Weyl's theorem
    Duggal, B
    Harte, R
    Jeon, IH
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2004, 132 (05) : 1345 - 1349
  • [18] On Weyl's Theorem for Functions of Operators
    Jiong DONG
    Xiao Hong CAO
    Lei DAI
    Acta Mathematica Sinica,English Series, 2019, (08) : 1367 - 1376
  • [19] Weyl's theorem for class A operators
    Uchiyama, A
    MATHEMATICAL INEQUALITIES & APPLICATIONS, 2001, 4 (01): : 143 - 150
  • [20] On Weyl’s Theorem for Functions of Operators
    Jiong Dong
    Xiao Hong Cao
    Lei Dai
    Acta Mathematica Sinica, English Series, 2019, 35 : 1367 - 1376