Jauch-Piron states on von Neumann algebras.
Kernel Operators on Lp-spaces Associated with Semifinite von Neumann Algebras.
KMS-symmetric Markov semigroups.
Kolmogoroff consistency theorem for Gleason measures
-spaces and quantum dynamical semigroups
La stabilité des espaces L... non-commutatifs.
Laws of large numbers in von Neumann algebras and related results
Les systèmes-produits et l'espace de Fock, d'après W. Arveson
Limit laws for Random matrices and free products.
Locally convex quasi C*-algebras and noncommutative integration
We continue the analysis undertaken in a series of previous papers on structures arising as completions of C*-algebras under topologies coarser that their norm topology and we focus our attention on the so-called locally convex quasi C*-algebras. We show, in particular, that any strongly *-semisimple locally convex quasi C*-algebra (𝔛,𝔄₀) can be represented in a class of noncommutative local L²-spaces.
Marcinkiewicz spaces, commutators and non-commutative geometry
Nigel J. Kalton was one of the most eminent guests participating in the Józef Marcinkiewicz Centenary Conference. His contribution to the scientific aspect of the meeting was very essential. Nigel was going to prepare a paper based on his plenary lecture. The editors are completely sure that the paper would be a real ornament of the Proceedings. Unfortunately, Nigel's sudden death totally destroyed editors' hopes and plans. Every mathematician knows how unique were Nigel's mathematical achievements....
Markov chains as Evans-Hudson diffusions in Fock space
Martingale convergence theorems in -algebras.
Measure theory in noncommutative spaces.
Measures on orthomodular vector space lattices
Multiplicative functions on the lattice of non-crossing partitions and free convolution.
Non-Commutative Banach Function Spaces.
Noncommutative function theory and unique extensions
We generalize, to the setting of Arveson’s maximal subdiagonal subalgebras of finite von Neumann algebras, the Szegő -distance estimate and classical theorems of F. and M. Riesz, Gleason and Whitney, and Kolmogorov. As a byproduct, this completes the noncommutative analog of the famous cycle of theorems characterizing the function algebraic generalizations of from the 1960’s. A sample of our other results: we prove a Kaplansky density result for a large class of these algebras, and give a necessary...
Noncommutative Orlicz spaces associated to a state
We introduce and study the noncommutative Orlicz spaces associated to a normal faithful state on a semifinite von Neumann algebra.
Noncommutative Poincaré recurrence theorem
Poincaré’s classical recurrence theorem is generalised to the noncommutative setup where a measure space with a measure-preserving transformation is replaced by a von Neumann algebra with a weight and a Jordan morphism leaving the weight invariant. This is done by a suitable reformulation of the theorem in the language of -space rather than the original measure space, thus allowing the replacement of the commutative von Neumann algebra by a noncommutative one.