Self-Conjugate Polyhedral Banach Spaces
Copyright policy )Self-Conjugate Polyhedral Banach Spaces
Problem 91 (of Mazur) in the Scottish Book asked whether a real finite- dimensional Banach space isometric to its dual is necessarily isometrically an inner-product space. Answering this in the negative, Sztencel and Zaremba asked whether self-conjugate normed spaces with polyhedral unit balls exist for dimensions \(n\geq 3.\) An affirmative answer to this question is given, first by a short argument involving direct sums and secondly by an inductive construction due to B. Grünbaum. It is also shown that uncountably many mutually non-isometric 3-dimensional self-conjugate spaces with polyhedral ball exist.
- University of Cambridge United Kingdom
Geometry and structure of normed linear spaces, Duality and reflexivity in normed linear and Banach spaces, self-conjugate normed spaces with polyhedral unit balls
Geometry and structure of normed linear spaces, Duality and reflexivity in normed linear and Banach spaces, self-conjugate normed spaces with polyhedral unit balls
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