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This article is cited in 23 scientific papers (total in 23 papers)
The Banach–Mazur Theorem for Spaces with Asymmetric Norm
P. A. Borodin M. V. Lomonosov Moscow State University
Abstract:
We establish an analog of the Banach–Mazur theorem for real separable linear spaces with asymmetric norm: every such space can be linearly and isometrically embedded in the space of continuous functions $f$ on the interval $[0,1]$ equipped with the asymmetric norm $\|f|=\max\{f(t)\colon t\in[0,1]\}$. This assertion is used to obtain nontrivial representations of an arbitrary convex closed body $M\subset\mathbb R^n$ , an arbitrary compact set $K\subset\mathbb R^n$, and an arbitrary continuous function $F\colon K\to\mathbb R$.
Received: 24.01.2000
Citation:
P. A. Borodin, “The Banach–Mazur Theorem for Spaces with Asymmetric Norm”, Mat. Zametki, 69:3 (2001), 329–337; Math. Notes, 69:3 (2001), 298–305
Linking options:
https://www.mathnet.ru/eng/mzm506https://doi.org/10.4213/mzm506 https://www.mathnet.ru/eng/mzm/v69/i3/p329
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