An extension of the normed dual functors

By means of the direct limit technique, with every normed space X it is associated a bidualic (Banach) space \(\tilde{X} (D^2( \tilde{X}) \cong \tilde{X} \) - called the hyperdual of \(X\)) that contains (isometrically embedded) \(X\) as well as all the even (normed) duals \(D^{2n}(X)\), which make...

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Bibliographic Details
Published in:arXiv.org 2019-05
Main Author: Uglesic, Nikica
Format: Article
Language:English
Online Access:Get full text
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Summary:By means of the direct limit technique, with every normed space X it is associated a bidualic (Banach) space \(\tilde{X} (D^2( \tilde{X}) \cong \tilde{X} \) - called the hyperdual of \(X\)) that contains (isometrically embedded) \(X\) as well as all the even (normed) duals \(D^{2n}(X)\), which make an increasing sequence of the category retracts. The algebraic dimension dim \(\tilde{X}\) = dim \(X\) (dim \(\tilde{X}\) = \(2^{\aleph_0}\) ), whenever dim \(X \neq \aleph_0\), (dim \(X = \aleph_0\)). Furthermore, the correspondence \(X \mapsto \tilde{X}\) extends to a faithful covariant functor (called the hyperdual functor) on the category of normed spaces.
ISSN:2331-8422