5,148 research outputs found

    An asymmetric Kadison's inequality

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    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

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    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

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    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

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    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 m:GCm: G \to \mathbb{C} 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 1p1 \le p \le \infty. Then, mHm_{\mid_H} yields an Lp-bounded Fourier multiplier on the group von Neumann algebra of H provided the modular function ΔH\Delta_H coincides with ΔG\Delta_G 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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