Riesz operators and the complete norm topology |
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Authors: | M Oudghiri |
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Institution: | Department of Mathematics, University Abdelmalek Essaadi, BP 2121, Tetouan, Morocco |
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Abstract: | We show that a non-injective Riesz operator on an infinite-dimensional Banach space X does not determine the complete norm topology of X. We also show that an injective operator with trivial generalized range determines the complete norm topology of X. Finally this result is used to settle the crucial role of the non-injectivity condition in our first result. |
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Keywords: | Riesz operator Decomposability Uniqueness of complete norm topology |
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