On i-opertators on real normed spaces
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Date
Authors
Garcia-Pacheco, Francisco Javier
Puglisi, Daniele
Van Zyl, Gusti
Journal Title
Journal ISSN
Volume Title
Publisher
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].
Description
Keywords
i-Operator, Real topological vector spaces, Real vector spaces, Real normed spaces, Cartesian
Sustainable Development Goals
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