377 research outputs found
Confluent operator algebras and the closability property
Certain operator algebras A on a Hilbert space have the property that every
densely defined linear transformation commuting with A is closable. Such
algebras are said to have the closability property. They are important in the
study of the transitive algebra problem. More precisely, if A is a
two-transitive algebra with the closability property, then A is dense in the
algebra of all bounded operators, in the weak operator topology. In this paper
we focus on algebras generated by a completely nonunitary contraction, and
produce several new classes of algebras with the closability property. We show
that this property follows from a certain strict cyclicity property, and we
give very detailed information on the class of completely nonunitary
contractions satisfying this property, as well as a stronger property which we
call confluence.Comment: Preliminary versio
MODELLING THE ELECTRON WITH COSSERAT ELASTICITY
Interactions between a finite number of bodies and the surrounding fluid, in a channel for instance, are investigated theoretically. In the planar model here the bodies or modelled grains are thin solid bodies free to move in a nearly parallel formation within a quasi-inviscid fluid. The investigation involves numerical and analytical studies and comparisons. The three main features that appear are a linear instability about a state of uniform motion, a clashing of the bodies (or of a body with a side wall) within a finite scaled time when nonlinear interaction takes effect, and a continuum-limit description of the bodyâfluid interaction holding for the case of many bodies
One-sided Cauchy-Stieltjes Kernel Families
This paper continues the study of a kernel family which uses the
Cauchy-Stieltjes kernel in place of the celebrated exponential kernel of the
exponential families theory. We extend the theory to cover generating measures
with support that is unbounded on one side. We illustrate the need for such an
extension by showing that cubic pseudo-variance functions correspond to
free-infinitely divisible laws without the first moment. We also determine the
domain of means, advancing the understanding of Cauchy-Stieltjes kernel
families also for compactly supported generating measures
Two Banach space methods and dual operator algebras
In this paper we present several new slightly nonlinear variants of the bipolar and the open mapping theorems in Banach spaces, which we abstracted from the recent developments in the theory of dual operator algebras.A new application of our techniques to the theory of operator algebras is also given.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/27530/1/0000574.pd
Dilation theory and systems of simultaneous equations in the predual of an operator algebra. II
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46272/1/209_2005_Article_BF01163170.pd
Intersections of Schubert varieties and eigenvalue inequalities in an arbitrary finite factor
It is known that the eigenvalues of selfadjoint elements a,b,c with a+b+c=0
in the factor R^omega (ultrapower of the hyperfinite II1 factor) are
characterized by a system of inequalities analogous to the classical Horn
inequalities of linear algebra. We prove that these inequalities are in fact
true for elements of an arbitrary finite factor. A matricial (`complete') form
of this result is equivalent to an embedding question formulated by Connes.Comment: 41 pages, many figure
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