Approximate identity and approximation properties of multidimensional Fourier algebras

TL;DR

This paper investigates the approximation properties, operator amenability, and weak amenability of multidimensional Fourier algebras associated with locally compact groups, extending classical harmonic analysis concepts.

Contribution

It introduces and analyzes the approximation identity and operator amenability for the multidimensional Fourier algebra $A^n(G)$, providing new insights into their structure and properties.

Findings

Characterization of approximation identity in $A^n(G)$

Conditions for operator amenability of $A^n(G)$

Results on weak amenability and approximation properties

Abstract

For a locally compact group $G$, let $A^n(G)$ denote the multidimensional Fourier algebra given by $ \otimes_{n}^{eh} A(G).$ This work explores the approximation identity and operator amenability of the algebra $A^n(G)$. Further, we study the approximation properties (AP) and the concept of weak amenability of the multidimensional Fourier algebra.