期刊论文详细信息
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 卷:433
Spectral continuity using v-convergence
Article
Sanchez-Perales, Salvador1  Djordjevic, Slavisa V.2 
[1] Univ Tecnol Mixteca, Inst Fis & Matemat, Oaxaca 69000, Mexico
[2] Benemerita Univ Autonoma Puebla, Fac Ciencias Fis Matemat, Puebla 72570, Pue, Mexico
关键词: The v-convergence;    Approximate point spectrum;    Continuity of the spectrum;   
DOI  :  10.1016/j.jmaa.2015.07.069
来源: Elsevier
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【 摘 要 】

Let T, T-n, n is an element of N, be bounded linear operators defined on a Banach space X such that {T-n} converges to T in v-convergence (this new mode of convergence was observed by Mario Ahues). In this paper, sufficient conditions are given for the convergence gamma(T-n) -> gamma(T), where gamma is an element of {sigma, sigma(ap)}. Also we give some conditions for a bounded operator S in order to have the stability of convergence: gamma(T-n + S) -> gamma(T + S). Among other things, we show that if 0 is an accumulation point of sigma(T) then sigma(T-n) -> sigma(T) when T-n,T satisfy the growth condition (G(1)). (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

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