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The V a -deformation of the classical convolution

Anna Dorota Krystek (2007)

Banach Center Publications

We study deformations of the classical convolution. For every invertible transformation T:μ ↦ Tμ, we are able to define a new associative convolution of measures by μ * T ν = T - 1 ( T μ * T ν ) . We deal with the V a -deformation of the classical convolution. We prove the analogue of the classical Lévy-Khintchine formula. We also show the central limit measure, which turns out to be the standard Gaussian measure. Moreover, we calculate the Poisson measure in the V a -deformed classical convolution and give the orthogonal polynomials...

The variational approach to the Dirichlet problem in C*-algebras

Fabio Cipriani (1998)

Banach Center Publications

The aim of this work is to develop the variational approach to the Dirichlet problem for generators of sub-Markovian semigroups on C*-algebras. KMS symmetry and the KMS condition allow the introduction of the notion of weak solution of the Dirichlet problem. We will then show that a unique weak solution always exists and that a generalized maximum principle holds true.

The von Neumann algebras generated by t -gaussians

Éric Ricard (2006)

Annales de l’institut Fourier

We study the t -deformation of gaussian von Neumann algebras. They appear as example in the theories of Interacting Fock spaces and conditionally free products. When the number of generators is fixed, it is proved that if t is sufficiently close to 1 , then these algebras do not depend on t . In the same way, the notion of conditionally free von Neumann algebras often coincides with freeness.

The weak Phillips property

Ali Ülger (2001)

Colloquium Mathematicae

Let X be a Banach space. If the natural projection p:X*** → X* is sequentially weak*-weak continuous then the space X is said to have the weak Phillips property. We present several characterizations of the spaces having this property and study its relationships to other Banach space properties, especially the Grothendieck property.

Toeplitz-Berezin quantization and non-commutative differential geometry

Harald Upmeier (1997)

Banach Center Publications

In this survey article we describe how the recent work in quantization in multi-variable complex geometry (domains of holomorphy, symmetric domains, tube domains, etc.) leads to interesting results and problems in C*-algebras which can be viewed as examples of the "non-commutative geometry" in the sense of A. Connes. At the same time, one obtains new functional calculi (of pseudodifferential type) with possible applications to partial differential equations and group representations.

Topologies on central extensions of von Neumann algebras

Shavkat Ayupov, Karimbergen Kudaybergenov, Rauaj Djumamuratov (2012)

Open Mathematics

Given a von Neumann algebra M, we consider the central extension E(M) of M. We introduce the topology t c(M) on E(M) generated by a center-valued norm and prove that it coincides with the topology of local convergence in measure on E(M) if and only if M does not have direct summands of type II. We also show that t c(M) restricted to the set E(M)h of self-adjoint elements of E(M) coincides with the order topology on E(M)h if and only if M is a σ-finite type Ifin von Neumann algebra.

Currently displaying 121 – 140 of 164