537 research outputs found
A Matrix Convexity Approach to Some Celebrated Quantum Inequalities
Some of the important inequalities associated with quantum entropy are
immediate algebraic consequences of the Hansen-Pedersen-Jensen inequality. A
general argument is given using matrix perspectives of operator convex
functions. A matrix analogue of Mar\'{e}chal's extended perspectives provides
additional inequalities, including a result of Lieb.Comment: 8 page
A new look at C*-simplicity and the unique trace property of a group
We characterize when the reduced C*-algebra of a group has unique tracial
state, respectively, is simple, in terms of Dixmier-type properties of the
group C*-algebra. We also give a simple proof of the recent result by
Breuillard, Kalantar, Kennedy and Ozawa that the reduced C*-algebra of a group
has unique tracial state if and only if the amenable radical of the group is
trivial.Comment: 8 page
Completely positive multipliers of quantum groups
We show that any completely positive multiplier of the convolution algebra of
the dual of an operator algebraic quantum group \G (either a locally compact
quantum group, or a quantum group coming from a modular or manageable
multiplicative unitary) is induced in a canonical fashion by a unitary
corepresentation of \G. It follows that there is an order bijection between
the completely positive multipliers of L^1(\G) and the positive functionals
on the universal quantum group C_0^u(\G). We provide a direct link between
the Junge, Neufang, Ruan representation result and the representing element of
a multiplier, and use this to show that their representation map is always
weak-weak-continuous.Comment: 18 pages; major rewrit
On the Grothendieck Theorem for jointly completely bounded bilinear forms
We show how the proof of the Grothendieck Theorem for jointly completely
bounded bilinear forms on C*-algebras by Haagerup and Musat can be modified in
such a way that the method of proof is essentially C*-algebraic. To this
purpose, we use Cuntz algebras rather than type III factors. Furthermore, we
show that the best constant in Blecher's inequality is strictly greater than
one.Comment: 9 pages, minor change
Skew Category Algebras Associated with Partially Defined Dynamical Systems
We introduce partially defined dynamical systems defined on a topological
space. To each such system we associate a functor from a category to
\Top^{\op} and show that it defines what we call a skew category algebra . We study the connection between topological freeness of
and, on the one hand, ideal properties of and, on
the other hand, maximal commutativity of in . In
particular, we show that if is a groupoid and for each e \in \ob(G) the
group of all morphisms is countable and the topological space
is Tychonoff and Baire, then the following assertions are equivalent:
(i) is topologically free; (ii) has the ideal intersection property,
that is if is a nonzero ideal of , then ; (iii) the ring is a maximal abelian complex subalgebra of . Thereby, we generalize a result by Svensson, Silvestrov
and de Jeu from the additive group of integers to a large class of groupoids.Comment: 16 pages. This article is an improvement of, and hereby a replacement
for, version 1 (arXiv:1006.4776v1) entitled "Category Dynamical Systems and
Skew Category Algebras
Noncommutative Figa-Talamanca-Herz algebras for Schur multipliers
We introduce a noncommutative analogue of the Fig\'a-Talamanca-Herz algebra
on the natural predual of the operator space of
completely bounded Schur multipliers on Schatten space . We determine the
isometric Schur multipliers and prove that the space of bounded
Schur multipliers on Schatten space is the closure in the weak operator
topology of the span of isometric multipliers.Comment: 24 pages; corrected typo
Structure, classifcation, and conformal symmetry, of elementary particles over non-archimedean space-time
It is known that no length or time measurements are possible in sub-Planckian
regions of spacetime. The Volovich hypothesis postulates that the
micro-geometry of spacetime may therefore be assumed to be non-archimedean. In
this letter, the consequences of this hypothesis for the structure,
classification, and conformal symmetry of elementary particles, when spacetime
is a flat space over a non-archimedean field such as the -adic numbers, is
explored. Both the Poincar\'e and Galilean groups are treated. The results are
based on a new variant of the Mackey machine for projective unitary
representations of semidirect product groups which are locally compact and
second countable. Conformal spacetime is constructed over -adic fields and
the impossibility of conformal symmetry of massive and eventually massive
particles is proved
Perturbations of nuclear C*-algebras
Kadison and Kastler introduced a natural metric on the collection of all
C*-subalgebras of the bounded operators on a separable Hilbert space. They
conjectured that sufficiently close algebras are unitarily conjugate. We
establish this conjecture when one algebra is separable and nuclear. We also
consider one-sided versions of these notions, and we obtain embeddings from
certain near inclusions involving separable nuclear C*-algebras. At the end of
the paper we demonstrate how our methods lead to improved characterisations of
some of the types of algebras that are of current interest in the
classification programme.Comment: 45 page
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