80 research outputs found
Simple purely infinite C*-algebras and n-filling actions
Let be a positive integer. We introduce a concept, which we call the
-filling property, for an action of a group on a separable unital
-algebra . If is a commutative unital -algebra and
the action is induced by a group of homeomorphisms of then the
-filling property reduces to a weak version of hyperbolicity. The
-filling property is used to prove that certain crossed product
-algebras are purely infinite and simple. A variety of group actions on
boundaries of symmetric spaces and buildings have the -filling property. An
explicit example is the action of on the projective
-space.Comment: 16 page
Property (RD) for Hecke pairs
As the first step towards developing noncommutative geometry over Hecke
C*-algebras, we study property (RD) (Rapid Decay) for Hecke pairs. When the
subgroup H in a Hecke pair (G,H) is finite, we show that the Hecke pair (G,H)
has (RD) if and only if G has (RD). This provides us with a family of examples
of Hecke pairs with property (RD). We also adapt Paul Jolissant's works in 1989
to the setting of Hecke C*-algebras and show that when a Hecke pair (G,H) has
property (RD), the algebra of rapidly decreasing functions on the set of double
cosets is closed under holomorphic functional calculus of the associated
(reduced) Hecke C*-algebra. Hence they have the same K_0-groups.Comment: A short note added explaining other methods to prove that the
subalgebra of rapidly decreasing functions is smooth. This is the final
version as published. The published version is available at: springer.co
Quantum Symmetries and Strong Haagerup Inequalities
In this paper, we consider families of operators in
a tracial C-probability space , whose joint
-distribution is invariant under free complexification and the action of
the hyperoctahedral quantum groups . We prove a strong
form of Haagerup's inequality for the non-self-adjoint operator algebra
generated by , which generalizes the
strong Haagerup inequalities for -free R-diagonal families obtained by
Kemp-Speicher \cite{KeSp}. As an application of our result, we show that
always has the metric approximation property (MAP). We also apply
our techniques to study the reduced C-algebra of the free unitary
quantum group . We show that the non-self-adjoint subalgebra generated by the matrix elements of the fundamental corepresentation of
has the MAP. Additionally, we prove a strong Haagerup inequality for
, which improves on the estimates given by Vergnioux's property
RD \cite{Ve}
New holomorphically closed subalgebras of -algebras of hyperbolic groups
We construct dense, unconditional subalgebras of the reduced group
-algebra of a word-hyperbolic group, which are closed under holomorphic
functional calculus and possess many bounded traces. Applications to the cyclic
cohomology of group -algebras and to delocalized -invariants of
negatively curved manifolds are given
The design of an adaptive optics telescope: the case of DAG
In this paper, we describe in detail the optical design of DAG, a new 4 m telescope for Turkey. DAG is an "adaptive optics friendly" telescope, in a sense that each design decision is taken considering the potential impact on the AO performance (vibrations, static aberrations etc.) The objective is to make this telescope fully ready for AO at first light. It is designed as a Ritchey-Chretien combination, 56 m focal length, with Nasmyth foci only, and active optics. Its total RMS error is expected to be 45 nm up to Zernike mode 78, and 26 nm for the higher, non AO corrected modes. A final design optimization has been done by the telescope manufacturers, demonstrating that our AO-based requirements can be satisfied, without much difficulty.Publisher's Versio
Speckle noise and dynamic range in coronagraphic images
This paper is concerned with the theoretical properties of high contrast
coronagraphic images in the context of exoplanet searches. We derive and
analyze the statistical properties of the residual starlight in coronagraphic
images, and describe the effect of a coronagraph on the speckle and photon
noise. Current observations with coronagraphic instruments have shown that the
main limitations to high contrast imaging are due to residual quasi-static
speckles. We tackle this problem in this paper, and propose a generalization of
our statistical model to include the description of static, quasi-static and
fast residual atmospheric speckles. The results provide insight into the
effects on the dynamic range of wavefront control, coronagraphy, active speckle
reduction, and differential speckle calibration. The study is focused on
ground-based imaging with extreme adaptive optics, but the approach is general
enough to be applicable to space, with different parameters.Comment: 31 pages, 18 figure
On twisted Fourier analysis and convergence of Fourier series on discrete groups
We study norm convergence and summability of Fourier series in the setting of
reduced twisted group -algebras of discrete groups. For amenable groups,
F{\o}lner nets give the key to Fej\'er summation. We show that Abel-Poisson
summation holds for a large class of groups, including e.g. all Coxeter groups
and all Gromov hyperbolic groups. As a tool in our presentation, we introduce
notions of polynomial and subexponential H-growth for countable groups w.r.t.
proper scale functions, usually chosen as length functions. These coincide with
the classical notions of growth in the case of amenable groups.Comment: 35 pages; abridged, revised and update
An E-ELT Case Study: Colour-Magnitude Diagrams of an Old Galaxy in the Virgo Cluster
One of the key science goals for a diffraction limited imager on an Extremely
Large Telescope (ELT) is the resolution of individual stars down to faint
limits in distant galaxies. The aim of this study is to test the proposed
capabilities of a multi-conjugate adaptive optics (MCAO) assisted imager
working at the diffraction limit, in IJHK filters, on a 42m diameter ELT to
carry out accurate stellar photometry in crowded images in an Elliptical-like
galaxy at the distance of the Virgo cluster. As the basis for realistic
simulations we have used the phase A studies of the European-ELT project,
including the MICADO imager (Davies & Genzel 2010) and the MAORY MCAO module
(Diolaiti 2010). We convolved a complex resolved stellar population with the
telescope and instrument performance expectations to create realistic images.
We then tested the ability of the currently available photometric packages
STARFINDER and DAOPHOT to handle the simulated images. Our results show that
deep Colour-Magnitude Diagrams (photometric error, 0.25 at I27.2;
H25. and K24.6) of old stellar populations in galaxies, at the
distance of Virgo, are feasible at a maximum surface brightness,
17 mag/arcsec (down to M and M M), and
significantly deeper (photometric error, 0.25 at I29.3; H26.6
and K26.2) for 21 mag/arcsec (down to M and
M M). The photometric errors, and thus also the depth of
the photometry should be improved with photometry packages specifically
designed to adapt to an ELT MCAO Point Spread Function. We also make a simple
comparison between these simulations and what can be expected from a Single
Conjugate Adaptive Optics feed to MICADO and also the James Webb Space
Telescope.Comment: 17 pages, 22 figures, accepted on A&
Fundamental limitations on Earth-like planet detection with Extremely Large Telescopes
We analyse the fundamental limitations for the detection of extraterrestrial
planets with Extremely Large Telescopes. For this task, a coronagraphic device
combined to a very high order wavefront correction system is required but not
sufficient to achieve the contrast level needed for detecting an
Earth-like planet. The stellar residuals left uncorrected by the wavefront
correction system need to be calibrated and subtracted. In this paper, we
consider a general model including the dynamic phase aberrations downstream the
wavefront correction system, the static phase aberrations of the instrument and
some differential aberrations provided by the calibration unit. A rather
optimistic case of a filled circular pupil and of a perfect coronagraph is
elsewhere assumed. As a result of the analytical study, the limitation mostly
comes from the static aberrations. Using numerical simulations we confirm this
result and evaluate the requirements in terms of phase aberrations to detect
Earth-like planets on Extremely Large Telescopes.Comment: 8 pages, 8 figures, accepted in A&
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