9,278 research outputs found

### An Extrapolation of Operator Valued Dyadic Paraproducts

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 $1<p<\infty$ implies their boundedness on L^p(\T,L^p(\M)) for all
$1<p<\infty$ 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

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

### An Extrapolation of Operator Valued Dyadic Paraproducts

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 $1<p<\infty$ implies their boundedness on L^p(\T,L^p(\M)) for all
$1<p<\infty$ 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

Let T be the unite circle on $R^2$. 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

We prove that $(\lambda_g\mapsto e^{-t|g|^r}\lambda_g)_{t>0}$ defines a
completely bounded semigroup of multipliers on the von Neuman algebra of
hyperbolic groups for all real number $r$. 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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