Invariant Means on $VN^n(G)$
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866912830029037568 |
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| author | Wadhawan, Kanupriya Kumar, N. Shravan |
| author_facet | Wadhawan, Kanupriya Kumar, N. Shravan |
| contents | Let $G$ be a locally compact group, and $VN^n(G)$ is the dual of the multidimensional Fourier algebra $A^n(G)$. In this article, we define invariant means on $VN^n(G)$ and prove that the set of all invariant means on $VN^n(G)$ is non-empty. Further, we investigated the invariant means on $VN^n(G)$ for discrete and non-discrete cases of $G$. Also, we show that if $H$ is an open subgroup of $G$, then the number of invariant means on $VN^n(H)$ is the same as that of $VN^n(G)$. Finally, we study invariant means on the dual of the algebra $A_0^n(G)$, the closure of Fourier algebra $A^n(G)$ in the cb-multiplier norm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_12063 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Invariant Means on $VN^n(G)$ Wadhawan, Kanupriya Kumar, N. Shravan Functional Analysis Let $G$ be a locally compact group, and $VN^n(G)$ is the dual of the multidimensional Fourier algebra $A^n(G)$. In this article, we define invariant means on $VN^n(G)$ and prove that the set of all invariant means on $VN^n(G)$ is non-empty. Further, we investigated the invariant means on $VN^n(G)$ for discrete and non-discrete cases of $G$. Also, we show that if $H$ is an open subgroup of $G$, then the number of invariant means on $VN^n(H)$ is the same as that of $VN^n(G)$. Finally, we study invariant means on the dual of the algebra $A_0^n(G)$, the closure of Fourier algebra $A^n(G)$ in the cb-multiplier norm. |
| title | Invariant Means on $VN^n(G)$ |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2601.12063 |