149 research outputs found
Orbits in symmetric spaces
We characterize those elements in a fully symmetric spaces on the interval
or on the semi-axis whose orbits are the norm-closed
convex hull of their extreme points. Our results extend and complement earlier
work on the same theme by Braverman and Mekler
Derivations in the Banach ideals of -compact operators
Let be a von Neumann algebra equipped with a faithful normal
semi-finite trace and let be the algebra of all
-compact operators affiliated with . Let be a symmetric operator space (on ) and let
be a symmetrically-normed Banach ideal of -compact
operators in . We study (i) derivations on
with the range in and (ii) derivations on the Banach algebra
. In the first case our main results assert that such derivations
are continuous (with respect to the norm topologies) and also inner (under some
mild assumptions on ). In the second case we show that any such
derivation is necessarily inner when is a type factor. As an
interesting application of our results for the case (i) we deduce that any
derivation from into an -space, ,
() associated with is inner
Commutator estimates in -factors
Let be a -factor and let be
the space of all measurable operators affiliated with . It is
shown that for any self-adjoint element there exists a
scalar , such that for all , there
exists a unitary element from , satisfying
. A corollary
of this result is that for any derivation on with the
range in an ideal , the derivation is inner,
that is , and . Similar
results are also obtained for inner derivations on .Comment: 21 page
On uniqueness of distribution of a random variable whose independent copies span a subspace in L_p
Let 1\leq p<2 and let L_p=L_p[0,1] be the classical L_p-space of all (classes
of) p-integrable functions on [0,1]. It is known that a sequence of independent
copies of a mean zero random variable f from L_p spans in L_p a subspace
isomorphic to some Orlicz sequence space l_M. We present precise connections
between M and f and establish conditions under which the distribution of a
random variable f whose independent copies span l_M in L_p is essentially
unique.Comment: 14 pages, submitte
Dixmier traces and some applications to noncommutative geometry
This is a survey of some recent advances in the theory of singular traces in
which the authors have played some part and which were inspired by questions
raised by the book of Alain Connes (Noncommutative Geometry, Academic Press
1994). There are some original proofs and ideas but most of the results have
appeared elsewhere. Detailed information on the contents is contained in the
Introduction.Comment: To appear in Russian Mathematical Surveys (in Russian). New version
corrects Latex problems, minor errors and reference
- β¦