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BOUNDED LINEAR OPERATORS ON SPACES IN NORMED DUALITY
Published online by Cambridge University Press: 01 January 2007
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.
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- Copyright © Glasgow Mathematical Journal Trust 2007
References
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