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Ranges of Products of Operators

Published online by Cambridge University Press:  20 November 2018

Sandy Grabiner
Sandy Grabiner*
Affiliation:
Claremont Graduate School, Claremont, California
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Suppose that T and A are bounded linear operators. In this paper we examine the relation between the ranges of A and TA, under various additional hypotheses on T and A. We also consider the dual problem of the relation between the null-spaces of T and AT; and we consider some cases where T or A are only closed operators. Our major results about ranges of bounded operators are summarized in the following theorem.

Theorem 1. Suppose that T is a bounded operator on a Banach space E and that A is a non-zero bounded operator from some Banach space to E.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 6 , December 1974 , pp. 1430 - 1441
Copyright
Copyright © Canadian Mathematical Society 1974

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