Abstract
In the article, we find new dilatation results on non-commutative \(L^p\) spaces. We prove that any self-adjoint, unital, positive measurable Schur multiplier on some \(B(L^2(\Sigma ))\) admits, for all \(1\leqslant p<\infty \), an invertible isometric dilation on some non-commutative \(L^p\)-space. We obtain a similar result for self-adjoint, unital, completely positive Fourier multiplier on VN(G), when G is a unimodular locally compact group. Furthermore, we establish multivariable versions of these results.
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Acknowledgements
I would like to thank Christian Le Merdy, my thesis supervisor for all his support and his help. The LmB receives support from the EIPHI Graduate School (contract ANR-17-EURE-0002)
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Duquet, C. Dilation properties of measurable Schur multipliers and Fourier multipliers. Positivity 26, 69 (2022). https://doi.org/10.1007/s11117-022-00933-x
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DOI: https://doi.org/10.1007/s11117-022-00933-x