On i-opertators on real normed spaces

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Authors

Garcia-Pacheco, Francisco Javier
Puglisi, Daniele
Van Zyl, Gusti

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NISC (Pty) Ltd and Taylor & Francis

Abstract

We gradually study i-operators on real vector spaces, on real topological vector spaces, and on real normed spaces. Among several things we prove the existence of real topological vector spaces (different from the James’ Space) that are free of continuous i-operators. We also prove that every real normed space can be equivalently renormed to be free of norm i-operators. Examples of spaces of continuous functions not admitting norm i-operators and whose unit sphere is free of convex subsets with non-empty interior relative to it are also found. Finally, we also provide some results on a problem posed by Wenzel in [10].

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Keywords

i-Operator, Real topological vector spaces, Real vector spaces, Real normed spaces, Cartesian

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Citation

Francisco Javier García-Pacheco, Daniele Puglisi & Gusti van Zyl (2015) On i-operators on real normed spaces, Quaestiones Mathematicae, 38:2, 257-270, DOI:10.2989/16073606.2014.982344