Ideals in the dual of introverted subspaces of $Ψ$-pseudomeasures
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929527386537984 |
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| author | Dabra, Arvish Lal, Rattan Kumar, N. Shravan |
| author_facet | Dabra, Arvish Lal, Rattan Kumar, N. Shravan |
| contents | Let $G$ be a locally compact group and $(Φ,Ψ)$ a complementary pair of Young functions satisfying the $Δ_2$-condition. Let $A_Φ(G)$ be the Orlicz analogue of the Figà-Talamanca Herz algebra $A_p(G).$ The dual of the algebra $A_Φ(G)$ is the space of $Ψ$-pseudomeasures, denoted by $PM_Ψ(G).$ For certain topologically introverted subspaces $\mathcal{A}$ of $PM_Ψ(G)$ and the Banach algebras $W_Φ(G)$ or $B_Φ(G),$ denoted by $\mathcal{B},$ we characterise the maximal regular left/right/two-sided ideals of the Banach algebras $\mathcal{A}^{'}$ and $\mathcal{B}^{''}$ considered with the Arens product. We further characterise the minimal left ideals of $\mathcal{A}^{'}$ and prove the necessary and sufficient conditions for the existence of minimal ideals in the algebras $A_Φ(G)$ and $\mathcal{B}.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_04528 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ideals in the dual of introverted subspaces of $Ψ$-pseudomeasures Dabra, Arvish Lal, Rattan Kumar, N. Shravan Functional Analysis Primary 43A15, 46J10, 46J20, Secondary 43A99 Let $G$ be a locally compact group and $(Φ,Ψ)$ a complementary pair of Young functions satisfying the $Δ_2$-condition. Let $A_Φ(G)$ be the Orlicz analogue of the Figà-Talamanca Herz algebra $A_p(G).$ The dual of the algebra $A_Φ(G)$ is the space of $Ψ$-pseudomeasures, denoted by $PM_Ψ(G).$ For certain topologically introverted subspaces $\mathcal{A}$ of $PM_Ψ(G)$ and the Banach algebras $W_Φ(G)$ or $B_Φ(G),$ denoted by $\mathcal{B},$ we characterise the maximal regular left/right/two-sided ideals of the Banach algebras $\mathcal{A}^{'}$ and $\mathcal{B}^{''}$ considered with the Arens product. We further characterise the minimal left ideals of $\mathcal{A}^{'}$ and prove the necessary and sufficient conditions for the existence of minimal ideals in the algebras $A_Φ(G)$ and $\mathcal{B}.$ |
| title | Ideals in the dual of introverted subspaces of $Ψ$-pseudomeasures |
| topic | Functional Analysis Primary 43A15, 46J10, 46J20, Secondary 43A99 |
| url | https://arxiv.org/abs/2404.04528 |