Borel structures coming from various topologies on $\mathbf{B}(\mathcal{H})$

Proceedings of the Japan Academy, Series A. Mathematical Sciences

article

Ghorban Ali Bagheri-Bardi¹  Minoo Khosheghbal-Ghorabayi¹ 

[1] Department of Mathematics, Faculty of Sciences, Persian Gulf University

关键词: von Neumann algebras;    operator valued functions;    -algebras;    measurability.Classical hypergeometric series;    binomial series;    telescoping method;    Pfaff transformation.Laplace transform;    power function;    analysis on cones;    Wishart distribution;    graphical model.Evans-Selberg potential;    Evans kernel;    potential-theoretically parabolic Riemann surface;    Green function;    Green kernel;    fundamental metric.;   

DOI  :  10.3792/pjaa.93.7

学科分类：数学（综合）

来源: Japan Academy

【 摘 要 】

Although there exist different types of (well-known) locally convex topologies on $\mathbf{B}(\mathcal{H})$, the notion of measurability on the set of operator valued functions $f:\Omega\to \mathbf{B}(\mathcal{H})$ is unique when $\mathcal{H}$ is separable (see [1]). In this current discussion we observe that unlike the separable case, in the non-separable case we have to face different types of measurability. Moreover the algebraic operations “ addition and product ” are not compatible with the set of operator valued measurable functions.

【 授权许可】

Unknown