9,288 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 implies their boundedness on L^p(\T,L^p(\M)) for all
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 the algebra of matrices. We consider the dyadic
paraproducts associated with valued functions , and show that
the norm of does not dominate uniformly over . We also consider paraproducts
associated with noncommutative martingales and prove that their boundedness on
bounded noncommutative % martingale spaces implies their boundedness on
bounded noncommutative % martingale spaces for all .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 implies their boundedness on L^p(\T,L^p(\M)) for all
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 . 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 defines a
completely bounded semigroup of multipliers on the von Neuman algebra of
hyperbolic groups for all real number . 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
- …