A Banach principle for semifinite von Neumann algebras.
A -algebra on Schur algebras.
A -algebraic Schoenberg theorem
Let be a -algebra, a compact abelian group, an action of by -automorphisms of the fixed point algebra of and the dense sub-algebra of -finite elements in . Further let be a linear operator from into which commutes with and vanishes on . We prove that is a complete dissipation if and only if is closable and its closure generates a -semigroup of completely positive contractions. These complete dissipations are classified in terms of certain twisted negative definite...
A -dynamical system with Dedekind zeta partition function and spontaneous symmetry breaking
In this paper we extend to arbitrary number fields a construction of Bost-Connes of a -dynamical system with spontaneous symmetry breaking and partition function the Riemann zeta function.
A characterization of commutativity for non-associative normed algebras.
A characterization of completely bounded multipliers of Fourier algebras
A Characterization of the State Space of Quantum Mechanics
A Class of C*-Algebras and Topological Markov Chains.
A Class of C*-algebras and Topological Markov Chains II: Reducible Chains and the Ext-functor for C*-algebras.
A class of simple tracially AF -algebras.
A classification of approximately finite real C*-algebras.
A classification of ideals in crossed products.
A classification result for simple real approximate interval algebras.
A classification theorem for nuclear purely infinite simple -algebras.
A comment on free group factors
Let M be a finite von Neumann algebra acting on the standard Hilbert space L²(M). We look at the space of those bounded operators on L²(M) that are compact as operators from M into L²(M). The case where M is the free group factor is particularly interesting.
A decomposition theorem for regular extensions of von Neumann algebras.
A direct approach to co-universal algebras associated to directed graphs.
A double commutant theorem for purely large C*-subalgebras of real rank zero corona algebras
Let 𝓐 be a unital separable simple nuclear C*-algebra such that ℳ (𝓐 ⊗ 𝓚) has real rank zero. Suppose that ℂ is a separable simple liftable and purely large unital C*-subalgebra of ℳ (𝓐 ⊗ 𝓚)/ (𝓐 ⊗ 𝓚). Then the relative double commutant of ℂ in ℳ (𝓐 ⊗ 𝓚)/(𝓐 ⊗ 𝓚) is equal to ℂ.
A Duality Between Hilbert Modules And Fields Of Hilbert Spaces.
-algebras and topology of mapping tori
The paper studies applications of -algebras in geometric topology. Namely, a covariant functor from the category of mapping tori to a category of -algebras is constructed; the functor takes continuous maps between such manifolds to stable homomorphisms between the corresponding -algebras. We use this functor to develop an obstruction theory for the torus bundles of dimension , and . In conclusion, we consider two numerical examples illustrating our main results.