Approximation theorems for positive operators on L p-spaces

Abstract

Let 1 < r ⩽ p < ∞. Approximation theorems for positive contractions in L ( L p(m), L r(n) ) are presented. The characterization of norm attaining extreme positive contractions is given. Note that these extreme operators are also exposed points of the positive part of the unit ball of L ( l p, l r ).