Gowers-Maurey’ s space and its conjugate space

Abstract

RECENTLY Gowers and Maurey constructed the first example of Banach space containing no unconditional basic sequence. We denote this space by X G , in this note. Using the results in ref. [1], some further studies and reconstructions of this space result in some satisfactory answers of a series of open questions in the Banach spaces theory. There is a general description about this remarkable development. Just as indicated in ref. [1], the most important characteristic of the Banach space X G is...