Symmetry and quasi-centrality of operator space projective tensor product

TL;DR

This paper investigates the symmetry, quasi-centrality, and unitary structure of the operator space projective tensor product of C*-algebras, establishing new properties and relationships with Banach space tensor products.

Contribution

It proves the symmetry of the operator space projective tensor product and explores its quasi-centrality and unitary group, extending understanding of its algebraic and topological properties.

Findings

A extasciitilde{}hat{ ext{ exttwosuperior}}{}{ ext{ exttwosuperior}}{}$ is symmetric.

A extasciitilde{}hat{ ext{ exttwosuperior}}{}{ ext{ exttwosuperior}}{} is a weakly Wiener algebra.

Discussion of quasi-centrality and the unitary group of A extasciitilde{}hat{ ext{ exttwosuperior}}{}{ ext{ exttwosuperior}}{}.

Abstract

For $C^{*}$-algebras $A$ and $B$, the operator space projective tensor product $A\hat{\otimes}B$ and the Banach space projective tensor product $A\otimes_{\gamma}B$ are shown to be symmetric. We also show that $A\hat{\otimes}B$ is weakly Wiener algebra. Finally, quasi-centrality, and the unitary group of $A\hat{\otimes}B$ are discussed.