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- W4327670918 abstract "Let $M$ be a von Neumann algebra equipped with a normal semi-finite faithful trace (nsf trace in short) and let $Tcolon Mto M$ be a contraction. We say that $T$ is absolutely dilatable if there exist another von Neumann algebra $M'$ equipped with a nsf trace, a $w^*$-continuous trace preserving unital $*$-homomorphim $Jcolon Mto M'$ and a trace preserving $*$-automomorphim $Ucolon M'to M'$ such that $T^k=E U^k J$ for all integer $kgeq 0$, where $Ecolon M'to M$ is the conditional expectation associated with $J$. Given a $sigma$-finite measure space $(Omega,mu)$, we characterize bounded Schur multipliers $phiin L^infty(Omega^2)$ such that the Schur multiplication operator $T_phicolon B(L^2(Omega))to B(L^2(Omega))$ is absolutely dilatable. In the separable case, they are characterized by the existence of a von Neumann algebra $N$ with a separable predual, equipped with a normalized normal faithful trace $tau_N$, and of a $w^*$-continuous essentially bounded function $dcolonOmegato N$ such that $phi(s,t)=tau_N(d(s)^*d(t))$ for almost every $(s,t)inOmega^2$." @default.
- W4327670918 created "2023-03-18" @default.
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- W4327670918 date "2023-03-15" @default.
- W4327670918 modified "2023-09-24" @default.
- W4327670918 title "A characterization of absolutely dilatable Schur multipliers" @default.
- W4327670918 doi "https://doi.org/10.48550/arxiv.2303.08436" @default.
- W4327670918 hasPublicationYear "2023" @default.
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