Regularizers of Closed Operators

Author:

Lin C.-S.

Abstract

Let X and Y be two Banach spaces and let B(X, Y) denote the set of bounded linear operators with domain X and range in 7. For T∈B(X, Y), let N(T) denote the null space and R(T) the range of T. J. I. Nieto [5, p. 64] has proved the following two interesting results. An operator T∈B(X, Y) has a left regularizer, i.e., there exists a Q∈B(Y, X) such that QT=I+A, where I is the identity on X and A∈B(X, X) is a compact operator, if and only if dim N(T)<∞ and R(T) has a closed complement.

Publisher

Canadian Mathematical Society

Subject

General Mathematics

Cited by 5 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. The perturbation of relatively open operators with reduced index;Mathematical Proceedings of the Cambridge Philosophical Society;1992-09

2. On the perturbation of unbounded linear operators with topologically complemented ranges;Journal of Functional Analysis;1990-09

3. Unilateral quasi-regularizers of closed operators;Mathematical Proceedings of the Cambridge Philosophical Society;1980-05

4. On the continuous linear image of a Banach space;Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics;1980-03

5. Annotated Bibliography on Generalized Inverses and Applications;Generalized Inverses and Applications;1976

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