Extremally distant normed spaces with additional restrictions

Author: Bakharev, F.

Source: Mathematical Notes, Volume 79, Number 3, March 2006 , pp. 314-326(13)

Publisher: Springer

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Abstract:

We study the relationship between the Banach—Mazur distance and the modified Banach—Mazur distance. We sharpen the Szarek theorem on the construction of invariant norms with specific properties and construct extremally distant normed spaces with norms invariant under groups of automorphisms of small cardinality. We prove that the trivial upper bound for the Banach—Mazur distance obtained in terms of the modified Banach—Mazur distance is order-sharp.

Keywords: normed space; invariant norm; upper bound; Banach—Mazur distance; modified Banach—Mazur distance; symmetry group; Banach space; random variable

Document Type: Research article

DOI: http://dx.doi.org/10.1007/s11006-006-0036-4

Affiliations: 1: Email: fbakharev@yandex.ru

Publication date: 2006-03-01