An extension of the Maurey Factorization Theorem

Abstract

ABSTRACTLet be such that , X, Y Banach spaces, a measure space and a bounded linear operator. The Maurey Factorization Theorem gives the necessary and sufficient condition that U can be factored under the form , where is bounded linear and. In this paper, we define two new classes of bounded linear operators : the class of all operators which satisfies the -Maurey factorization, i.e. there exists and a -summing operator such that and the class of -Maurey operators. Our main result, which extends the Maurey Factorization Theorem, asserts that these two classes coincide. Under the assumptions that Y has cotype 2 we prove the equality between the class of operators with values in which satisfies the -Maurey factorization, the class of -Maurey operators, the class of S-almost summing operators and the class of -summing operators. Applications are given.