Non-Commutative HE(A; ℓ1) and HE(A; ℓ1) Spaces

Abstract

In this paper, we introduce non-commutative HE(A; ℓ1) and HE(A; ℓ1) spaces. Then HE(A; ℓ1) and HE(A; ℓ1) are shown to a possess many of the properties of non-commutative Hp(A) spaces, such as various factorization results including a Riesz type factorization theorem and contractibility of conditional expectation on these spaces.