Non-commutative Markov processes in free groups factors, related to Berezin's quantization and automorphic forms.
Non-commutative martingale VMO-spaces
We study Banach space properties of non-commutative martingale VMO-spaces associated with general von Neumann algebras. More precisely, we obtain a version of the classical Kadets-Pełczyński dichotomy theorem for subspaces of non-commutative martingale VMO-spaces. As application we prove that if ℳ is hyperfinite then the non-commutative martingale VMO-space associated with a filtration of finite-dimensional von Neumannn subalgebras of ℳ has property (u).
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.
Noncommutative spectral geometry of Riemannian foliations.
Non-commutative symmetric Markov semigroups.
Noncommutative weak Orlicz spaces and martingale inequalities
This paper is devoted to the study of noncommutative weak Orlicz spaces and martingale inequalities. The Marcinkiewicz interpolation theorem is extended to include noncommutative weak Orlicz spaces as interpolation classes. As an application, we prove the weak type Φ-moment Burkholder-Gundy inequality for noncommutative martingales through establishing a weak type Φ-moment noncommutative Khinchin inequality for Rademacher random variables.
Non-equilibrium phase transitions, coherence and chaos
We present a scheme for the theory of phase transitions in open dissipative systems, and show that its demands are fulfilled by quantum stochastic models of open systems, such as the laser.
Non-Hausdorff groupoids, proper actions and -theory.
Nonlinear Lie-type derivations of von Neumann algebras and related topics
Motivated by the powerful and elegant works of Miers (1971, 1973, 1978) we mainly study nonlinear Lie-type derivations of von Neumann algebras. Let 𝓐 be a von Neumann algebra without abelian central summands of type I₁. It is shown that every nonlinear Lie n-derivation of 𝓐 has the standard form, that is, can be expressed as a sum of an additive derivation and a central-valued mapping which annihilates each (n-1)th commutator of 𝓐. Several potential research topics related to our work are also...
Non-normal elements in Banach *-algebras
Let A be a Banach *-algebra with an identity, continuous involution, center Z and set of self-adjoint elements Σ. Let h ∈ Σ. The set of v ∈ Σ such that (h + iv)ⁿ is normal for no positive integer n is dense in Σ if and only if h ∉ Z. The case where A has no identity is also treated.
Non-orbit equivalent actions of
For any , we construct a concrete 1-parameter family of non-orbit equivalent actions of the free group . These actions arise as diagonal products between a generalized Bernoulli action and the action , where is seen as a subgroup of .
Non-self-adjoint operator algebras and inverse systems of simplicial complexes.
Nonstable K-Theory Results for Some AH-Algebras.
Non-trivial derivations on commutative regular algebras.
Necessary and sufficient conditions are given for a (complete) commutative algebra that is regular in the sense of von Neumann to have a non-zero derivation. In particular, it is shown that there exist non-zero derivations on the algebra L(M) of all measurable operators affiliated with a commutative von Neumann algebra M, whose Boolean algebra of projections is not atomic. Such derivations are not continuous with respect to measure convergence. In the classical setting of the algebra S[0,1] of all...
Norm attaining bilinear forms on C*-algebras
We give a sufficient condition on a C*-algebra to ensure that every weakly compact operator into an arbitrary Banach space can be approximated by norm attaining operators and that every continuous bilinear form can be approximated by norm attaining bilinear forms. Moreover we prove that the class of C*-algebras satisfying this condition includes the group C*-algebras of compact groups.
Norm inequalities in star algebras.
Normal cones and --convex structure
The notion of normal cones is used to characterize --convex algebras among unital, symmetric and complete -convex algebras.
Normal generation of unitary groups of Cuntz algebras by involutions.
Normal states and representations of the canonical commutation relations