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arXiv · 1903.06459

On the duals of normed spaces and quotient shapes

Nikica Uglesic
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Abstract

Some properties of the (normed) dual Hom-functor $D$ and its iterations $D^n$ are exhibited. For instance: $D$ turns every canonical embedding (in the second dual space) into a retraction (of the third dual onto the first one); $D$ rises the countably infinite (algebraic) dimension only; $D$ does not change the finite quotient shape type. By means of that, the finite quotient shape classification of normed vectorial spaces is completely solved. As a consequence, two extension type theorems are derived.

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Nikica Uglesic. 2019-03-15. On the duals of normed spaces and quotient shapes. https://arxiv.org/abs/1903.06459

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