A Banach principle for semifinite von Neumann algebras.
A generalized Biane process
A linear Radon-Nikodym type theorem for -algebras with applications to measure theory
A non-commutative central limit theorem.
A noncommutative version of a Theorem of Marczewski for submeasures
It is shown that every monocompact submeasure on an orthomodular poset is order continuous. From this generalization of the classical Marczewski Theorem, several results of commutative Measure Theory are derived and unified.
A nonsmooth exponential
Let ℳ be a type II₁ von Neumann algebra, τ a trace in ℳ, and L²(ℳ,τ) the GNS Hilbert space of τ. If L²(ℳ,τ)₊ is the completion of the set of selfadjoint elements, then each element ξ ∈ L²(ℳ,τ)₊ gives rise to a selfadjoint unbounded operator on L²(ℳ,τ). In this note we show that the exponential exp: L²(ℳ,τ)₊ → L²(ℳ,τ), , is continuous but not differentiable. The same holds for the Cayley transform . We also show that the unitary group with the strong operator topology is not an embedded submanifold...
A note on Lebesgue type decomposition for covariant completely positive maps on -algebras.
A Prokhorov's theorem for Banach lattice valued measures.
Algèbres de von Neumann de groupes libres et probabilités non commutatives
Almost sure convergence of iterates of contractions in noncommutative L2-spaces.
An Analogue of a Hardy-Littlewood-Fejér Inequality for Upper Triangular Trace Class Operators.
An individual ergodic theorem on the Hilbert space logic
Application du «bébé Fock» au modèle d'Ising
Applications du théorème de factorisation pour des fonctions à valeurs opérateurs
Arens algebras, associated with commutative von Neumann algebras
Automorphisms of central extensions of type I von Neumann algebras
Given a von Neumann algebra M we consider its central extension E(M). For type I von Neumann algebras, E(M) coincides with the algebra LS(M) of all locally measurable operators affiliated with M. In this case we show that an arbitrary automorphism T of E(M) can be decomposed as , where is an inner automorphism implemented by an element a ∈ E(M), and is a special automorphism generated by an automorphism ϕ of the center of E(M). In particular if M is of type then every band preserving automorphism...
Banach principle in the space of τ-measurable operators
We establish a non-commutative analog of the classical Banach Principle on the almost everywhere convergence of sequences of measurable functions. The result is stated in terms of quasi-uniform (or almost uniform) convergence of sequences of measurable (with respect to a trace) operators affiliated with a semifinite von Neumann algebra. Then we discuss possible applications of this result.
Banach-Saks properties in symmetric spaces of measurable operators
We study Banach-Saks properties in symmetric spaces of measurable operators. A principal result shows that if the symmetric Banach function space E on the positive semiaxis with the Fatou property has the Banach-Saks property then so also does the non-commutative space E(ℳ,τ) of τ-measurable operators affiliated with a given semifinite von Neumann algebra (ℳ,τ).
Bibounded operators on W*-algebras.
Bounded elements and spectrum in Banach quasi *-algebras
A normal Banach quasi *-algebra (,) has a distinguished Banach *-algebra consisting of bounded elements of . The latter *-algebra is shown to coincide with the set of elements of having finite spectral radius. If the family () of bounded invariant positive sesquilinear forms on contains sufficiently many elements then the Banach *-algebra of bounded elements can be characterized via a C*-seminorm defined by the elements of ().