Conditional expectation on non-commutative $H_p^{(r,s)}(\mathcal{A};{\ell }_{\infty })$ and $H_p(\mathcal{A};{\ell }_1)$ spaces : semifinite case

Abstract

In this paper we investigate the conditional expectation on the non-commutative $H_p^{(r,s)}(\mathcal{A};{\ell }_{\infty })$ and $H_p(\mathcal{A};{\ell }_1)$ spaces associated with semifinite subdiagonal algebra, and prove the contractibility of the underlying conditional expectation on these spaces.