5,148 research outputs found
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
Miscellaneous Applications of Quons
This paper deals with quon algebras or deformed oscillator algebras, for
which the deformation parameter is a root of unity. We show the interest of
such algebras for fractional supersymmetric quantum mechanics, angular momentum
theory and quantum information. More precisely, quon algebras are used for (i)
a realization of a generalized Weyl-Heisenberg algebra from which it is
possible to associate a fractional supersymmetric dynamical system, (ii) a
polar decomposition of SU_2 and (iii) a construction of mutually unbiased bases
in Hilbert spaces of prime dimension. We also briefly discuss (symmetric
informationally complete) positive operator valued measures in the spirit of
(iii).Comment: This is a contribution to the Proc. of the 3-rd Microconference
"Analytic and Algebraic Methods III"(June 19, 2007, Prague, Czech Republic),
published in SIGMA (Symmetry, Integrability and Geometry: Methods and
Applications) at http://www.emis.de/journals/SIGMA
Manifold interpolation and model reduction
One approach to parametric and adaptive model reduction is via the
interpolation of orthogonal bases, subspaces or positive definite system
matrices. In all these cases, the sampled inputs stem from matrix sets that
feature a geometric structure and thus form so-called matrix manifolds. This
work will be featured as a chapter in the upcoming Handbook on Model Order
Reduction (P. Benner, S. Grivet-Talocia, A. Quarteroni, G. Rozza, W.H.A.
Schilders, L.M. Silveira, eds, to appear on DE GRUYTER) and reviews the
numerical treatment of the most important matrix manifolds that arise in the
context of model reduction. Moreover, the principal approaches to data
interpolation and Taylor-like extrapolation on matrix manifolds are outlined
and complemented by algorithms in pseudo-code.Comment: 37 pages, 4 figures, featured chapter of upcoming "Handbook on Model
Order Reduction
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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