Auerbach Bases and Minimal Volume Sufficient Enlargements

DOI10.4153/CMB-2011-043-3zbMATH Open1247.46012arXiv1103.0997OpenAlexW2138725142MaRDI QIDQ3103587

Mikhail Ostrovskii

Publication date: 7 December 2011

Published in: Canadian Mathematical Bulletin (Search for Journal in Brave)

Abstract: Let $B_Y$ denote the unit ball of a normed linear space $Y$. A symmetric, bounded, closed, convex set $A$ in a finite dimensional normed linear space $X$ is called a {it sufficient enlargement} for $X$ if, for an arbitrary isometric embedding of $X$ into a Banach space $Y$, there exists a linear projection $P:YoX$ such that $P(B_Y)subsetA$. Each finite dimensional normed space has a minimal-volume sufficient enlargement which is a parallelepiped, some spaces have "exotic" minimal-volume sufficient enlargements. The main result of the paper is a characterization of spaces having "exotic" minimal-volume sufficient enlargements in terms of Auerbach bases.

Full work available at URL: https://arxiv.org/abs/1103.0997

zbMATH Keywords

Auerbach basissufficient enlargement

Mathematics Subject Classification ID

Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces (46B15) Asymptotic theory of convex bodies (52A23) Asymptotic theory of Banach spaces (46B06)

Related Items (3)

Sufficient enlargements of minimal volume for finite-dimensional normed linear spaces ⋮ Title not available (Why is that?) ⋮ On the Size of Minimum Super Arrovian Domains

This page was built for publication: Auerbach Bases and Minimal Volume Sufficient Enlargements

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q3103587)