9,278 research outputs found

    An Extrapolation of Operator Valued Dyadic Paraproducts

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    We consider the dyadic paraproducts \pi_\f on \T associated with an \M-valued function \f. Here \T is the unit circle and \M is a tracial von Neumann algebra. We prove that their boundedness on L^p(\T,L^p(\M)) for some 1<p<1<p<\infty implies their boundedness on L^p(\T,L^p(\M)) for all 1<p<1<p<\infty provided \f is in an operator-valued BMO space. We also consider a modified version of dyadic paraproducts and their boundedness on $L^p(\T,L^p(\M))

    Notes on Matrix Valued Paraproducts

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    Denote by MnM_n the algebra of n×nn\times n matrices. We consider the dyadic paraproducts πb\pi_b associated with MnM_n valued functions bb, and show that the L(Mn)L^\infty (M_n) norm of bb does not dominate πbL2(n2)L2(n2)||\pi_b||_{L^2(\ell _n^2)\to L^2(\ell_n^2)} uniformly over nn. We also consider paraproducts associated with noncommutative martingales and prove that their boundedness on bounded noncommutative LpL^p-% martingale spaces implies their boundedness on bounded noncommutative LqL^q-% martingale spaces for all 1<p<q<1<p<q<\infty .Comment: 12 page

    An Extrapolation of Operator Valued Dyadic Paraproducts

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    We consider the dyadic paraproducts \pi_\f on \T associated with an \M-valued function \f. Here \T is the unit circle and \M is a tracial von Neumann algebra. We prove that their boundedness on L^p(\T,L^p(\M)) for some 1<p<1<p<\infty implies their boundedness on L^p(\T,L^p(\M)) for all 1<p<1<p<\infty provided \f is in an operator-valued BMO space. We also consider a modified version of dyadic paraproducts and their boundedness on $L^p(\T,L^p(\M))

    BMO is the intersection of two translates of dyadic BMO

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    Let T be the unite circle on R2R^2. Denote by BMO(T) the classical BMO space and denote by BMO_D(T) the usual dyadic BMO space on T. We prove that, BMO(T) is the intersction of BMO_D(T) and a translate of BMO_D(T).Comment: 4 page

    Complete boundedness of the Heat Semigroups on the von Neumann Algebra of hyperbolic groups

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    We prove that (λgetgrλg)t>0(\lambda_g\mapsto e^{-t|g|^r}\lambda_g)_{t>0} defines a completely bounded semigroup of multipliers on the von Neuman algebra of hyperbolic groups for all real number rr. One ingredient in the proof is the observation that a construction of Ozawa allows to characterize the radial multipliers that are bounded on every hyperbolic graph, partially generalizing results of Haagerup--Steenstrup--Szwarc and Wysocza\'nski. Another ingredient is an upper estimate of trace class norms for Hankel matrices, which is based on Peller's characterization of such norms.Comment: v2: 28 pages, with new examples, new results, motivations and hopefully a better presentatio
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