In this talk we will investigate the structure of a class of closable derivations on von Neumann algebras coming from group-measure space constructions. We will then show how to apply these results to obtain new examples of von Neumann algebras which do not arise as group-measure space constructions, for example the von Neumann algebra L(SL3(Z) ∗G) where G is any non-trivial group. Results in g...

Theorem: An AW*-algebra is the ring generated by its projections if and only if it has no abelian summand. Corollary: Every equivalence in an A W*-algebra may be implemented by a partial isometry in the ring generated by the projections of the algebra. The corollary is extended to certain finite Baer »-rings. An early proposition in the theory of von Neumann algebras is that every such algebra ...

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We prove that for all 1 ≤ p ≤ ∞, p 6= 2, the Lp spaces associated to two von Neumann algebrasM, N are isometrically isomorphic if and only if M and N are Jordan *-isomorphic. This follows from a noncommutative Lp Banach-Stone theorem: a specific decomposition for surjective isometries of noncommutative Lp spaces.

We prove that the von Neumann algebras generated by n q-Gaussian elements, are factors for n > 2.

We introduce the notion of the Fourier and Fouier-Stieltjes algebra of a topological ∗-semigroup and show that these are commutative Banach algebras. For a class of foundation semigroups, we show that these are preduals of von Neumann algebras. 1. Definitions and Notations Let S be a locally compact topological semigroup and M(S) be the Banach algebra of all bounded regular Borel measures μ on ...

We introduce a relative index for a pair of dissipative operators in a von Neumann algebra of finite type and prove an analog of the Birman-Schwinger principle in this setting. As an application of this result, revisiting the Birman-Krein formula in the abstract scattering theory, we represent the de la Harpe-Skandalis determinant of the characteristic function of dissipative operators in the a...

We consider commuting squares of finite dimensional von Neumann algebras having the algebra of complex numbers in the lower left corner. Examples include the vertex models, the spin models (in the sense of subfactor theory) and the commuting squares associated to finite dimensional Kac algebras. To any such commuting square we associate a compact Kac algebra and we compute the corresponding sub...

We prove that for the relative entropy of faithful normal states φ and ω on the von Neumann algebra M the formula S(φ,ω) = sup{ω(Λ)-logφ(/): h = h*eM] holds. In general von Neumann algebras the relative entropy was defined and investigated by Araki [1, 3]. After Lieb had proved the joint convexity of the relative entropy in the type / case [10] several proofs appeared in the literature and they...

The present article contains a short introduction to Modular Theory for von Neumann algebras with a cyclic and separating vector. It includes the formulation of the central result in this area, the Tomita-Takesaki theorem, and several of its consequences. We illustrate this theory through several elementary examples. We also present more elaborate examples and compute modular objects for a disc...