About tensor products of Hilbert quasi *-algebras and their representability properties

TL;DR

This paper explores the tensor product of Hilbert quasi *-algebras, showing it retains key properties and that representability is preserved under tensor products of functionals.

Contribution

It introduces a construction for tensor products of Hilbert quasi *-algebras that preserves their structure and representability properties.

Findings

Tensor product of two Hilbert quasi *-algebras is again a Hilbert quasi *-algebra.

Representability properties are maintained in the tensor product.

Tensor product of representable and continuous functionals remains representable.

Abstract

This note aims to investigate the tensor product of two given Hilbert quasi *-algebras and its properties. The construction proposed in this note turns out to be again a Hilbert quasi *-algebra, thus interesting representability properties studed in \cite{AT} are maintained. Furthermore, if two functionals are representable and continuous respectively on the two Hilbert quasi *-algebras, then so is their tensor product.