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Approximate identity and approximation properties of multidimensional Fourier algebras

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Kanupriya, N. Shravan Kumar

Functional Analysis · Submitted 8 Jan 2025

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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 $A^n(G)$.

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arXiv ID2501.04351 (version 1)
Pith IDGGV3YGYO, Pith's permanent record of this paper and its review
CitationKanupriya, N. Shravan Kumar. "Approximate identity and approximation properties of multidimensional Fourier algebras." arXiv:2501.04351 (2025). https://pith.science/paper/GGV3YGYO
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,347 input tokens.

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arXiv listing abstract v1. Results and the main claim are underlined; .

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.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 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 $A^n(G)$. contribution 0.76 0.55 0.12 asserted 0.87
s1 Further, we study the approximation properties (AP) and the concept of weak amenability of the multidimensional Fourier algebra. contribution 1.00 0.83 0.08 asserted 0.90

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Original 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.

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