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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Minimal projections and absolute projection constants for regular polyhedral spaces


Authors: Bruce L. Chalmers and Boris Shekhtman
Journal: Proc. Amer. Math. Soc. 95 (1985), 449-452
MSC: Primary 51M20; Secondary 46B20
MathSciNet review: 806085
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Abstract: Let $ V = [{v_1}, \ldots ,{v_n}]$ be the $ n$-dimensional space of coordinate functions on a set of points $ \tilde v \subset {{\mathbf{R}}^n}$ where $ \tilde v$ is the set of vertices of a regular convex polyhedron. In this paper the absolute projection constant of any $ n$-dimensional Banach space $ E$ isometrically isomorphic to $ V \subset C(\tilde v)$ is computed, examples of which are the well-known cases $ E = l_n^\infty ,l_n^1$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0806085-4
PII: S 0002-9939(1985)0806085-4
Article copyright: © Copyright 1985 American Mathematical Society