A class of extreme contractions inL(l p )

Abstract

In this note we prove that: if T is a contraction in L(lp) that maps elements of disjoint support to elements of disjoint support, then T is an extreme point of the unit ball of L(lp), 1<p < ∞, p ≠ 2, if and only if T is of the form $$T = \sum\limits_{i = 1}^\infty {\delta _i \otimes y_i } $$ , where either (yi) form a p-orthonormal sequence or the nonzero elements of (yi) form a p-orthonormal sequence for which $$\mathop \cup \limits_i $$ supp (yi)=N.