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Regularizers of Closed Operators

Published online by Cambridge University Press:  20 November 2018

C.-S. Lin
C.-S. Lin*
Affiliation:
University of New Brunswick, Fredericton, N.B.
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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.

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 1 , 01 March 1974 , pp. 67 - 71
Copyright
Copyright © Canadian Mathematical Society 1974

References

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