Minimality properties of Tsirelson type spaces

2007/02/08 by Kutzarova, Denka, Leung, Denny, Manoussakis, Antonis +1
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.math/0702210

Abstract

In this paper, we study minimality properties of partly modified mixed Tsirelson spaces. A Banach space with a normalized basis (e_k) is said to be subsequentially minimal if for every normalized block basis (x_k) of (e_k), there is a further block (y_k) of (x_k) such that (y_k) is equivalent to a subsequence of (e_k). Sufficient conditions are given for a partly modified mixed Tsirelson space to be subsequentially minimal and connections with Bourgain's ℓ¹-index are established. It is also shown that a large class of mixed Tsirelson spaces fails to be subsequentially minimal in a strong sense.

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