Banach spaces which are far from all lattices (Q1412296)

This is a lecture with the description of some results of the following papers: \textit{Y. Gordon} and \textit{M. Junge} [Positivity 1, 7--43 (1997; Zbl 0911.46010), Stud. Math. 136, 147--182 (1999; Zbl 0952.46008)], and \textit{N. J. Nielsen} [Positivity 1, 359--379 (1997; Zbl 0902.46004)], \textit{Y. Gordon, M. Meyer} and \textit{A. Pajor} [Ill. J. Math. 40, 91--107 (1996; Zbl 0843.46008)]. The author considers the volume ratio values of an \(n\)-dimensional Banach space \(X\) with respect to ellipsoids and to zonoids and the connection of this ratio with the local unconditional structure constant of \(X\).