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• W2982415293 abstract "Abstract Using probabilistic tools, we prove that any weak* continuous semigroup $(T_t)_{t geqslant 0}$ of self-adjoint unital completely positive measurable Schur multipliers acting on the space $mathrm {B}({mathrm {L}}^2(X))$ of bounded operators on the Hilbert space ${mathrm {L}}^2(X)$ , where X is a suitable measure space, can be dilated by a weak* continuous group of Markov $*$ -automorphisms on a bigger von Neumann algebra. We also construct a Markov dilation of these semigroups. Our results imply the boundedness of the McIntosh’s ${mathrm {H}}^infty $ functional calculus of the generators of these semigroups on the associated Schatten spaces and some interpolation results connected to ${mathrm {BMO}}$ -spaces. We also give an answer to a question of Steen, Todorov, and Turowska on completely positive continuous Schur multipliers." @default.
• W2982415293 created "2019-11-08" @default.
• W2982415293 creator A5015704792 @default.
• W2982415293 date "2023-04-05" @default.
• W2982415293 modified "2023-10-16" @default.
• W2982415293 title "Dilations of Markovian semigroups of measurable Schur multipliers" @default.
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• W2982415293 doi "https://doi.org/10.4153/s0008414x23000214" @default.
• W2982415293 hasPublicationYear "2023" @default.
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