Weakly compact operators on non-complete normed spaces |
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Authors: | Juan Francisco Mena Jurado,Á ngel Rodri´ guez Palacios |
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Affiliation: | Facultad de Ciencias, Departamento de Análisis Matemático, Universidad de Granada, 18071 Granada, Spain |
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Abstract: | We prove that weakly compact operators on a non-reflexive normed space cannot be bijective. We also show that, in the above result, bijectivity cannot be relaxed to surjectivity. Finally, we study the behaviour of surjective weakly compact operators on a non-reflexive normed space, when they are perturbed by small scalar multiples of the identity, and derive from this study the recent result of Spurný [A note on compact operators on normed linear spaces, Expo. Math. 25 (2007) 261–263] that compact operators on an infinite-dimensional normed space cannot be surjective. |
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Keywords: | 47B07 46B10 |
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