General semifinite factor representations of the diffeomorphism group of euclidean space are constructed by means of a canonical correspondence with the finite factor representations of the inductive limit unitary group. This construction includes the quasi-free representations of the canonical commutation and anti-commutation relations. To establish this correspondence requires a non-linear fo...

The notion of (unbounded) C∗-seminorms plays a relevant role in the representation theory of ∗-algebras and partial ∗-algebras. A rather complete analysis of the case of ∗-algebras has given rise to a series of interesting concepts like that of semifinite C∗seminorm and spectral C∗-seminorm that give information on the properties of ∗-representations of the given ∗-algebra A and also on the str...

We study semifinite harmonic functions on the zigzag graph, which corresponds to Pieri rule for fundamental quasisymmetric $$\{F_{\lambda}\}$$ . The main problem, we solve here, is classify indecomposable this graph. show that these are in a natural bijective correspondence with some combinatorial data, so-called growth models. Furthermore, describe an explicit construction produces function fr...

We initiate the large scale geometric study of Banach-Lie groups, especially linear groups. show that exponential length, originally introduced by Ringrose for unitary groups $C^*$-algebras, defines quasi-isometry type any connected group. As an illustrative example, we consider separable abelian unital $C^*$-algebras with spectrum having finitely many components, which classify up to topologic...

It is known that, for a positive Dunford-Schwartz operator in noncommutative L p -space, 1 ? < ? , or, more generally, Orlicz space with order continuous norm, the corresponding ergodic averages converge bilaterally almost uniformly. We show that these blaterally uniformly each symmetric E such ? t ( x ) ? 0 as every ? where non-increasing rearrangement of . Noncommutative Dunford-Schwartz-type...