Positive isometric Fourier multipliers on non-commutative $L^p$-spaces
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866908872989474816 |
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| author | Kriegler, Christoph Merdy, Christian Le Zadeh, Safoura |
| author_facet | Kriegler, Christoph Merdy, Christian Le Zadeh, Safoura |
| contents | For a locally compact group \(G\), let \(\mathcal{L}G\) denote its left group von Neumann algebra and let \(L^p(\mathcal{L}G)\), \(1 \le p \le \infty\), be the corresponding non-commutative \(L^p\)-space. Given \(ϕ\in L^\infty(G)\), we study the Fourier multiplier \(M_{ϕ,p}\) acting on \(L^p(\mathcal{L}G)\). We prove that for any \(p \neq 2\), the operator \(M_{ϕ,p}\) is a positive surjective isometry if and only if \(ϕ\) coincides locally almost everywhere with a continuous character of \(G\). This characterization extends results obtained recently (jointly with C.~Arhancet) in the unimodular setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_07754 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Positive isometric Fourier multipliers on non-commutative $L^p$-spaces Kriegler, Christoph Merdy, Christian Le Zadeh, Safoura Operator Algebras For a locally compact group \(G\), let \(\mathcal{L}G\) denote its left group von Neumann algebra and let \(L^p(\mathcal{L}G)\), \(1 \le p \le \infty\), be the corresponding non-commutative \(L^p\)-space. Given \(ϕ\in L^\infty(G)\), we study the Fourier multiplier \(M_{ϕ,p}\) acting on \(L^p(\mathcal{L}G)\). We prove that for any \(p \neq 2\), the operator \(M_{ϕ,p}\) is a positive surjective isometry if and only if \(ϕ\) coincides locally almost everywhere with a continuous character of \(G\). This characterization extends results obtained recently (jointly with C.~Arhancet) in the unimodular setting. |
| title | Positive isometric Fourier multipliers on non-commutative $L^p$-spaces |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2603.07754 |