We study Michael’s lower semifinite topology and Fell’s topology on the collection of all closed limit subsets of a topological space. Special attention is given to the subfamily of all maximal limit sets.

The Kubo–Ando theory deals with connections for positive bounded operators. On the other hand, in various analysis related to von Neumann algebras, it is impossible avoid unbounded In this paper, we try extend a notion of cover classes operators (or objects such as forms and weights) appearing naturally setting must keep all expected properties maintained. This generalization carried out follow...

The Sierpinski gasket admits a locally isometric ramified self-covering. A semifinite spectral triple is constructed on the resulting solenoidal space, and its main geometrical features are discussed.

We review the recent construction of semifinite spectral triples for graph C∗algebras. These examples have inspired many other developments and we review some of these such as the relation between the semifinite index and the Kasparov product, examples of noncommutative manifolds, and an index theorem in twisted cyclic theory using a KMS state. Alan L. Carey Mathematical Sciences Institute Aust...

We study semifinite harmonic functions on arbitrary branching graphs. give a detailed exposition of an algebraic method which allows one to classify indecomposable some multiplicative It was suggested by A. Wassermann in terms operator algebras, but we rephrase, clarify, and simplify the main arguments working only with combinatorial objects. This work inspired theory traceable factor represent...

Connes and Cuntz showed in [Comm. Math. Phys. 114 (1988), 515–526] that suitable cyclic cocycles can be represented as Chern characters of finitely summable semifinite Fredholm modules. We show an analogous result in twisted cyclic cohomology using Chern characters of modular Fredholm modules. We present examples of modular Fredholm modules arising from Podleś spheres and from SUq(2).

A result of H.-W. Wiesbrock is extended from the case of a common cyclic and separating vector for the half-sided modular inclusion N ⊂ M of von Neumann algebras to the case of a common faithful normal semifinite weight and at the same time a gap in Wiesbrock’s proof is filled in.

We determine when there is a unique conditional expectation from a semifinite von Neumann algebra onto a singly-generated maximal abelian *-subalgebra. Our work extends the results of Kadison and Singer via new methods, notably the observation that a unique conditional expectation onto a singly-generated maximal abelian *-subalgebra must be normal.

We prove a factorization of completely bounded maps from a C *-algebra A (or an exact operator space E ⊂ A) to ℓ 2 equipped with the operator space structure of (C, R) θ (0 < θ < 1) obtained by complex interpolation between the column and row Hilbert spaces. More precisely, if F denotes ℓ 2 equipped with the operator space structure of (C, R) θ , then u : A → F is completely bounded iff there a...

We fully describe the doubly stochastic orbit of a self-adjoint element in noncommutative $$L_1$$ -space affiliated with semifinite von Neumann algebra, which answers problem posed by Alberti and Uhlmann (Stochasticity partial order: maps unitary mixing. VEB Deutscher Verlag der Wissenschaften, Berlin, 1982) 1980s, extending several results literature. It follows further from our methods that, ...