The Walsh basis in the Lp-spaces of hyperfinite III_\lambda-factors, 0 < \lambda <= 1

TL;DR

This paper introduces a non-commutative Walsh system and proves it forms a Schauder basis in Lp-spaces of hyperfinite III_actors, advancing understanding of non-commutative harmonic analysis.

Contribution

It presents the first construction of a non-commutative Walsh basis in the context of hyperfinite III_actors and establishes its basis properties in Lp-spaces.

Findings

The Walsh system forms a Schauder basis in Lp-spaces for 1 < p < .

The construction applies to hyperfinite III_actors with 0 <                        .

Abstract

We introduce a non-commutative Walsh system and prove that it forms a Schauder basis in the Lp-spaces (1 < p < \infty) associated with the hyperfinite III_\lambda-factors (0 < \lambda <= 1).