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We show that for any strongly closed subgroup of a unitary group of a finite von Neumann algebra, there exists a canonical Lie algebra which is complete with respect to the strong resolvent topology. Our analysis is based on the comparison between measure topology induced by the tracial state and the strong resolvent topology we define on the particular space of closed operators on the Hilbert space. This is an expository article of the paper by both authors in Hokkaido Math. J. 41 (2012), 31-99,...
Consider a simple non-compact algebraic group, over any locally compact non-discrete field, which has Kazhdan’s property . For any such group, , we present a Kazhdan set of two elements, and compute its best Kazhdan constant. Then, settling a question raised by Serre and by de la Harpe and Valette, explicit Kazhdan constants for every lattice in are obtained, for a “geometric” generating set of the form , where is a ball of radius , and the dependence of on is described explicitly....
We consider exponential functionals of a brownian motion with drift in ℝn, defined via a collection of linear functionals. We give a characterisation of the Laplace transform of their joint law as the unique bounded solution, up to a constant factor, to a Schrödinger-type partial differential equation. We derive a similar equation for the probability density. We then characterise all diffusions which can be interpreted as having the law of the brownian motion with drift conditioned on the law of...
Generalizing the proof – by Hecht and Schmid – of Osborne’s conjecture we prove an Archimedean (and weaker) version of a theorem of Colette Moeglin. The result we obtain is a precise Archimedean version of the general principle – stated by the second author – according to which a local Arthur packet contains the corresponding local -packet and representations which are more tempered.
We prove some extension theorems involving uniformly continuous maps of the universal Urysohn space. As an application, we prove reconstruction theorems for certain groups of autohomeomorphisms of this space and of its open subsets.
On munit la classe des algèbres de Kac d’une nouvelle classe de morphismes, stable par dualité. Cela permet de rendre compte, dans les cas abélien ou symétrique, de la catégorie des groupes localement compacts munis des morphismes continus de groupe. Le lien avec les morphismes précédemment définis et beaucoup plus restrictifs est établi.
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