On the Banach-Mazur Type for Normed Spaces

Details On the Banach-Mazur Type for Normed Spaces On the Banach-Mazur Type for Normed Spaces

2008-12-11

arxiv.org/abs/0812.2216v2

Ulmer Seminare 14, 2009, 317-324

Mathematics

Functional Analysis

9 pages; added proper tribute to some original work due to Banach and Mazur

Scientific paper

In order to measure qualitative properties we introduce a notion of a type for arbitrary normed spaces which measures the worst possible growth of partial sums of sequences weakly converging to zero. The ideas can be traced back to Banach and Mazur who used this type to compare the so-called linear dimension of classical Banach spaces. As an application we compare the linear dimension and investigate isomorphy of some classical Banach spaces.

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