A uniformly convex Banach space whose subspaces fail Gordon-Lewis property
In 1993, the famous \textit{W. T. Gowers} and \textit{B. Maurey} example of a hereditary indecomposable Banach space appeared [J. Am. Math. Soc. 6, No. 4, 851-874 (1993; Zbl 0827.46008)]. Subsequently a lot of work was done to improve their construction. Thus, Ferenczi presented an example of a uniformly convex hereditarily indecomposable space, and Habala obtained an example of a Banach space all subspaces of which fail the Gordon-Lewis property; his space also turned out to be hereditarily indecomposable. In this paper the authors construct a uniformly convex hereditarily indecomposable space all subspaces of which fail the Gordon-Lewis property.
scientific article; zbMATH DE number 1292439