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 | |
【 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】
Free
【 预 览 】
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