Conditional expectation on non-commutative $H^{(r,s)}_{p}(\mathcal A;\ell_{\infty})$ and $H_{p}(\mathcal A;\ell_{1})$ spaces : semifinite case

TL;DR

This paper studies the properties of conditional expectation operators on specific non-commutative Hardy spaces associated with semifinite subdiagonal algebras, proving their contractibility.

Contribution

It establishes the contractibility of conditional expectations on non-commutative Hardy spaces in the semifinite setting, extending understanding of their structure.

Findings

Conditional expectations are contractive on these spaces.

The work extends classical results to non-commutative semifinite algebras.

Provides new tools for analysis in non-commutative harmonic analysis.

Abstract

In this paper we investigate the conditional expectation on the non-commutative $H^{(r,s)}_{p}(\mathcal A;\ell_{\infty})$ 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.