In this paper we study the metric geometry of the space Σ of positive invertible elements of a von Neumann algebra. A with a finite, normal and faithful tracial state T. The trace induces an incomplete Riemannian  metric ...

For a semi-finite von Neumann algebra A, we study the case of equality in Young´s inequality of s-numbers for a pair of τ-measurable operators a,b, and we prove that equality is only possible if |a|^p=|b|^q. We also extend ...

Let A be a von Neumann algebra and PA the manifold of projections in A. There is a natural linear connection in PA, which in the finite dimensional case coincides with the the Levi-Civita connection of the Grassmann manifold ...

In this paper we introduce a family of examples that can be regarded as spaces of nonpositive curvature, but with the distinct quality that they are not complete as metric spaces. This amounts to the fact that they are ...

This note presents a new proof of the fact that every uniformly bounded group of invertible elements in a finite von Neumann algebra is similar to a unitary group. In 1974, Vasilescu and Zsido proved this result using the ...

We study the geometry of the set Ip = v ∈ M: v∗v = p of partial isometries of a finite von Neumann algebra M, with initial space p (p is a projection of the algebra). This set is a C∞ submanifold of M in the norm topology ...

Let A be a von Neumann algebra with a finite trace , represented in H = L2(A, ), and let Bt ⊂ A be sub- algebras, for t in an interval I (0 ∈ I). Let Et : A → Bt be the unique -preserving conditional expectation. We say ...