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BOUNDED LINEAR OPERATORS ON SPACES IN NORMED DUALITY

Published online by Cambridge University Press:  01 January 2007

BRUCE A. BARNES
BRUCE A. BARNES*
Affiliation:
Dept. of Math., Univ. of Oregon, Eugene, OR 97403, USA e-mail: barnes@math.oregon.edu
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Abstract.

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Let T be a bounded linear operator on a Banach space W, assume W and Y are in normed duality, and assume that T has adjoint T† relative to Y. In this paper, conditions are given that imply that for all λ≠0, λ−T and λ −T† maintain important standard operator relationships. For example, under the conditions given, λ −T has closed range if, and only if, λ −T† has closed range.

These general results are shown to apply to certain classes of integral operators acting on spaces of continuous functions.

Keywords

47A05
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 49 , Issue 1 , January 2007 , pp. 145 - 154
Copyright
Copyright © Glasgow Mathematical Journal Trust 2007

References

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