In this paper, we study the descriptive complexity of some inevitable
classes of Banach spaces. Precisely, as shown in [Go], every Banach
space either contains a hereditarily indecomposable subspace or an unconditional
basis, and, as shown in [FR], every Banach space either contains a minimal
subspace or a continuously tight subspace. In these notes, we study the complexity of those inevitable classes as well as the complexity of containing a subspace in any of those classes.
History
Publisher Statement
This is the author’s version of a work that was accepted for publication in Journal of Mathematical Analysis and Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Mathematical Analysis and Applications. 2015. 431(1): 682-701. DOI: 10.1016/j.jmaa.2015.05.045.