84 research outputs found
Some remarks on noncommutative Khintchine inequalities
Normalized free semi-circular random variables satisfy an upper Khintchine
inequality in . We show that this implies the corresponding upper
Khintchine inequality in any noncommutative Banach function space. As
applications, we obtain a very simple proof of a well-known interpolation
result for row and column operator spaces and, moreover, answer an open
question on noncommutative moment inequalities concerning a paper by Bekjan and
Chen
Transfer of Fourier multipliers into Schur multipliers and sumsets in a discrete group
We inspect the relationship between relative Fourier multipliers on
noncommutative Lebesgue-Orlicz spaces of a discrete group and relative
Toeplitz-Schur multipliers on Schatten-von-Neumann-Orlicz classes. Four
applications are given: lacunary sets; unconditional Schauder bases for the
subspace of a Lebesgue space determined by a given spectrum, that is, by a
subset of the group; the norm of the Hilbert transform and the Riesz projection
on Schatten-von-Neumann classes with exponent a power of 2; the norm of
Toeplitz Schur multipliers on Schatten-von-Neumann classes with exponent less
than 1.Comment: Corresponds to the version published in the Canadian Journal of
Mathematics 63(5):1161-1187 (2011
Complex interpolation of weighted noncommutative -spaces
Let be a semifinite von Neumann algebra equipped with a
semifinite normal faithful trace . Let be an injective positive
measurable operator with respect to such that is
also measurable. Define
We show that for 1\le p_0,
and the interpolation equality
holds with equivalent norms, where
and
.Comment: To appear in Houston J. Mat
An asymmetric Kadison's inequality
Some inequalities for positive linear maps on matrix algebras are given,
especially asymmetric extensions of Kadison's inequality and several operator
versions of Chebyshev's inequality. We also discuss well-known results around
the matrix geometric mean and connect it with complex interpolation.Comment: To appear in LA
Higher order extension of L\"owner's theory: Operator -tone functions
The new notion of operator/matrix -tone functions is introduced, which is
a higher order extension of operator/matrix monotone and convex functions.
Differential properties of matrix -tone functions are shown.
Characterizations, properties, and examples of operator -tone functions are
presented. In particular, integral representations of operator -tone
functions are given, generalizing familiar representations of operator monotone
and convex functions.Comment: final version, 33 page
A Markov dilation for self-adjoint Schur multipliers
We give a formula for Markov dilation in the sense of Anantharaman-Delaroche
for real positive Schur multipliers on \B(H)Comment: To appear in proceedings of am
Noncommutative de Leeuw theorems
Let H be a subgroup of some locally compact group G. Assume H is approximable
by discrete subgroups and G admits neighborhood bases which are
"almost-invariant" under conjugation by finite subsets of H. Let be a bounded continuous symbol giving rise to an Lp-bounded Fourier
multiplier (not necessarily cb-bounded) on the group von Neumann algebra of G
for some . Then, yields an Lp-bounded Fourier
multiplier on the group von Neumann algebra of H provided the modular function
coincides with over H. This is a noncommutative form of
de Leeuw's restriction theorem for a large class of pairs (G,H), our
assumptions on H are quite natural and recover the classical result. The main
difference with de Leeuw's original proof is that we replace dilations of
gaussians by other approximations of the identity for which certain new
estimates on almost multiplicative maps are crucial. Compactification via
lattice approximation and periodization theorems are also investigated
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