8,880 research outputs found
Noncommutative topology and Jordan operator algebras
Jordan operator algebras are norm-closed spaces of operators on a Hilbert
space with for all . We study noncommutative topology,
noncommutative peak sets and peak interpolation, and hereditary subalgebras of
Jordan operator algebras. We show that Jordan operator algebras present perhaps
the most general setting for a `full' noncommutative topology in the
C*-algebraic sense of Akemann, L. G. Brown, Pedersen, etc, and as modified for
not necessarily selfadjoint algebras by the authors with Read, Hay and other
coauthors. Our breakthrough relies in part on establishing several strong
variants of C*-algebraic results of Brown relating to hereditary subalgebras,
proximinality, deeper facts about for a left ideal in a C*-algebra,
noncommutative Urysohn lemmas, etc. We also prove several other approximation
results in -algebras and various subspaces of -algebras, related to
open and closed projections, and technical -algebraic results of Brown.Comment: Revision, many typos corrected and exposition improved in places.
Section 2 expanded with some applications of the main theorem of that sectio
Metric characterizations II
The present paper is a sequel to our paper "Metric characterization of
isometries and of unital operator spaces and systems". We characterize certain
common objects in the theory of operator spaces (unitaries, unital operator
spaces, operator systems, operator algebras, and so on), in terms which are
purely linear-metric, by which we mean that they only use the vector space
structure of the space and its matrix norms. In the last part we give some
characterizations of operator algebras (which are not linear-metric in our
strict sense described in the paper).Comment: Presented at the AMS/SAMS Satellite Conference on Abstract Analysis,
University of Pretoria, South Africa, 5-7 December 2011. Revision of
2/24/2012 (Examples after theorem 3.2 added
The Status of Inelastic Dark Matter
In light of recent positive results from the DAMA experiment, as well as new
null results from CDMS Soudan, Edelweiss, ZEPLIN-I and CRESST, we reexamine the
framework of inelastic dark matter with a standard halo. In this framework,
which was originally introduced to reconcile tensions between CDMS and DAMA,
dark matter particles can scatter off of nuclei only by making a transition to
a nearly degenerate state that is roughly 100 \kev heavier. We find that
recent data significantly constrains the parameter space of the framework, but
that there are still regions consistent with all experimental results. Due to
the enhanced annual modulation and dramatically different energy dependence in
this scenario, we emphasize the need for greater information on the dates of
data taking, and on the energy distribution of signal and background. We also
study the specific case of ``mixed sneutrino'' dark matter, and isolate regions
of parameter space which are cosmologically interesting for that particular
model. A significant improvement in limits by heavy target experiments such as
ZEPLIN or CRESST should be able to confirm or exclude the inelastic dark matter
scenario in the near future. Within the mixed sneutrino model, an elastic
scattering signature should be seen at upcoming germanium experiments,
including future results from CDMS Soudan.Comment: 8 pages, 5 figures; updated to include CRESST results; version to
appear in Phys.Rev.
Open partial isometries and positivity in operator spaces
We study positivity in C*-modules and operator spaces using open tripotents,
and an ordered version of the `noncommutative Shilov boundary'. Because of
their independent interest, we also systematically study open tripotents and
their properties.Comment: To appea
- …