ASPECTS OF BOUNDED PERTURBATION THEORY
作者:
ERIC MARTENS,
期刊:
Quaestiones Mathematicae
(Taylor Available online 1976)
卷期:
Volume 1,
issue 1
页码: 1-18
ISSN:1607-3606
年代: 1976
DOI:10.1080/16073606.1976.9632512
出版商: Taylor & Francis Group
数据来源: Taylor
摘要:
This paper is concerned with the stability of certain properties of linear operators in locally convex topological vector spaces under perturbations by operators which aresmallin some sense. Section 3 deals with the very useful concept of Banach balls which was introduced by Raĭkov [9]. Some properties are discussed. The following section investigates the invertibility of certain operators generalizing results of Robert [10] and de Bruyn [2],[3]. These results are used extensively in the sequel. We go on to discuss Riesz operators. We obtain results stronger than those of de Bruyn [1] with regard to asymptotically quasi-compact operators in locally convex spaces. The proofs are basically adaptations of those from [1]. In the final section we observe some results concerning the range ad null space of an operator perturbed byboundedoperators. We obtain a result very similar to an unproved theorem of Vladimirskiĭ [a] and point out their differences. MOS codes 4601, 4710, 4745, 4768, 4755.
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