Even infinite dimensional real Banach spaces

Details Even infinite dimensional real Banach spaces Even infinite dimensional real Banach spaces

2007-04-11

arxiv.org/abs/0704.1459v1

Mathematics

Functional Analysis

22 pages

Scientific paper

This article is a continuation of a paper of the first author \cite{F} about complex structures on real Banach spaces. We define a notion of even infinite dimensional real Banach space, and prove that there exist even spaces, including HI or unconditional examples from \cite{F} and $C(K)$ examples due to Plebanek \cite{P}. We extend results of \cite{F} relating the set of complex structures up to isomorphism on a real space to a group associated to inessential operators on that space, and give characterizations of even spaces in terms of this group. We also generalize results of \cite{F} about totally incomparable complex structures to essentially incomparable complex structures, while showing that the complex version of a space defined by S. Argyros and A. Manoussakis \cite{AM} provide examples of essentially incomparable complex structures which are not totally incomparable.

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