We show that the reflexive lattice generated by a double triangle lattice of projections in a finite von Neumann algebra is topologically homeomorphic to the two-dimensional sphere S 2 (plus two distinct points corresponding to zero and I ).

In this note, we characterise completely the ideals of the groupoid C* -algebra arising from the asymptotic equivalence relation on the points of a Smale space and show that the related Ruelle algebra is simple when the Smale space is topologically transitive.

Let L be the complete lattice generated by a nest N on an infinite-dimensional separable Hilbert space H and a rank one projection P ξ given by a vector ξ in H. Assume that ξ is a separating vector for N , the core of the nest algebra Alg(N ). We show that L is a Kadison-Singer lattice, and hence the corresponding algebra Alg(L) is a Kadison-Singer algebra. We also describe the center of Alg(L) and its commutator modulo itself, and show that every bounded derivation from Alg(L) into itself is inner, and all n-th bounded cohomology groups H n (Alg(L), B(H)) of Alg(L) with coefficients in B(H) are trivial for all n 1.

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We investigate the continuity of (α, β)-derivations on B(X) or C * -algebras. We give some sufficient conditions on which (α, β)derivations on B(X) are continuous and show that each (α, β)-derivation from a unital C * -algebra into its a Banach module is continuous when α and β are continuous at zero. As an application, we also study the ultraweak continuity of (α, β)-derivations on von Neumann algebras.

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Abstract. We show that the stable C * -algebra and the related Ruelle algebra defined by I. Putnam from the irreducible Smale space associated with a topologically mixing expanding map of a compact metric space are strongly Morita equivalent to the groupoid C * -algebras defined directly from the expanding map by C. Anantharaman-Delaroche and V. Deaconu. As an application, we calculate the K * -group of the Ruelle algebra for a solenoid.

No abstract