8,149 research outputs found
Group C*-algebras as compact quantum metric spaces
Let be a length function on a group , and let denote the
operator of pointwise multiplication by on \bell^2(G). Following
Connes, can be used as a ``Dirac'' operator for . It
defines a Lipschitz seminorm on , which defines a metric on the state
space of . We investigate whether the topology from this metric
coincides with the weak-* topology (our definition of a ``compact quantum
metric space''). We give an affirmative answer for when
is a word-length, or the restriction to of a norm on
. This works for twisted by a 2-cocycle, and thus for
non-commutative tori. Our approach involves Connes' cosphere algebra, and an
interesting compactification of metric spaces which is closely related to
geodesic rays.Comment: 53 pages, yet more minor improvements. To appear in Doc. Mat
Topological convolution algebras
In this paper we introduce a new family of topological convolution algebras
of the form , where is a Borel
semi-group in a locally compact group , which carries an inequality of the
type for where pre-assigned,
and is a constant. We give a sufficient condition on the measures
for such an inequality to hold. We study the functional calculus and
the spectrum of the elements of these algebras, and present two examples, one
in the setting of non commutative stochastic distributions, and the other
related to Dirichlet series.Comment: Corrected version, to appear in Journal of Functional Analysi
Complex velocity transformations and the Bisognano--Wichmann theorem for quantum fields acting on Krein spaces
It is proven that in indefinite metric quantum field theory there exists a
dense set of analytic vectors for the generator of the one parameter group of
x^0-x^1 velocity transformations. This makes it possible to define complex
velocity transformations also for the indefinite metric case. In combination
with the results of Bros -- Epstein -- Moschella, proving Bisognano--Wichmann
(BW) analyticity within the linear program, one then obtains a suitable
generalization of the BW theorem for local, relativistic quantum fields acting
on Krein spaces ("quantum fields with indefinite metric")
Non Commutative Arens Algebras and their Derivations
Given a von Neumann algebra with a faithful normal semi-finite trace
we consider the non commutative Arens algebra and the related algebras
and
which are proved to be complete metrizable locally
convex *-algebras. The main purpose of the present paper is to prove that any
derivation of the algebra is inner and all
derivations of the algebras and
are spatial and implemented by elements of Comment: 19 pages. Submitted to Journal of Functional analysi
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