A note on the gl constant ofE $$\mathop \otimes \limits^ \vee $$ F F

Abstract

LetX andY be Banach spaces. TFAE (1)X andY do not contain subspaces uniformly isomorphic to\(l_\infty ^n ,s.\) (2) The local unconditional structure constant of the space of bounded operatorsL (X*k,Y k) tends to infinity for every increasing sequence\(\left\{ {X_k } \right\}_{k = 1}^\infty \) and\(\left\{ {Y_k } \right\}_{k = 1}^\infty \) of finite-dimensional subspaces ofX andY respectively.