Geodesic
BOUNDED LINEAR OPERATORS ON SPACES IN NORMED DUALITY
Glasgow mathematical journal, Tome 49 (2007) no. 1, pp. 145-154

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DOI

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.
DOI : 10.1017/S0017089507003503
Mots-clés : 47A05 
BARNES, BRUCE A. BOUNDED LINEAR OPERATORS ON SPACES IN NORMED DUALITY. Glasgow mathematical journal, Tome 49 (2007) no. 1, pp. 145-154. doi: 10.1017/S0017089507003503
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     title = {BOUNDED {LINEAR} {OPERATORS} {ON} {SPACES} {IN} {NORMED} {DUALITY}},
     journal = {Glasgow mathematical journal},
     pages = {145--154},
     year = {2007},
     volume = {49},
     number = {1},
     doi = {10.1017/S0017089507003503},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089507003503/}
}
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