Orthogonal Forms and Probability in von Neumann Algebras.
Comparision of states and Darboux-type properties in von Neumann algebras.
Convergence of orthogonal series of projections in Banach spaces
For a sequence of mutually orthogonal projections in a Banach space, we discuss all possible limits of the sums in a “strong” sense. Those limits turn out to be some special idempotent operators (unbounded, in general). In the case of X = L₂(Ω,μ), an arbitrary unbounded closed and densely defined operator A in X may be the μ-almost sure limit of (i.e. μ-a.e. for all f ∈ (A)).
Almost sure approximation of unbounded operators in
The possibilities of almost sure approximation of unbounded operators in by multiples of projections or unitary operators are examined.
Reinsurance-a new approach
We describe a new model of multiple reinsurance. The main idea is that the reinsurance premium is paid conditionally. It is motivated by some analysis of the ultimate price of the reinsurance contract. For simplicity we assume that the underlying risk pricing functional is the L₂-norm. An unexpected relation to the general theory of sample regularity of stochastic processes is given.
Compatibility and statistical inference for data in measurement model of Foulis and Randall
The bundle convergence in von Neumann algebras and their -spaces
A stronger version of almost uniform convergence in von Neumann algebras is introduced. This "bundle convergence" is additive and the limit is unique. Some extensions of classical limit theorems are obtained.
The unconditional pointwise convergence of orthogonal seriesin over a von Neumann algebra
The paper is devoted to some problems concerning a convergence of pointwise type in the -space over a von Neumann algebra M with a faithful normal state Φ [3]. Here is the completion of M under the norm .
Dilation theorems for completely positive maps and map-valued measures
The Stinespring theorem is reformulated in terms of conditional expectations in a von Neumann algebra. A generalisation for map-valued measures is obtained.
Page 1