Haagerup approximation property for arbitrary von Neumann algebras

TL;DR

This paper introduces a new way to define the Haagerup approximation property for any von Neumann algebra using its standard form and establishes how this property is inherited.

Contribution

It proposes a generalized definition of the Haagerup approximation property applicable to all von Neumann algebras and proves related heredity results.

Findings

Defined the Haagerup approximation property via standard form.

Proved heredity results for the property.

Extended the property to arbitrary von Neumann algebras.

Abstract

We attempt presenting a notion of the Haagerup approximation property for an arbitrary von Neumann algebra by using its standard form. We also prove the expected heredity results for this property.