Towards a Galois theory for crossed products of C*-algebras.
Towards a non-selfadjoint version of Kadison's theorem.
Trace inequalities for spaces in spectral duality
Let (A,e) and (V,K) be an order-unit space and a base-norm space in spectral duality, as in noncommutative spectral theory of Alfsen and Shultz. Let t be a norm lower semicontinuous trace on A, and let φ be a nonnegative convex function on ℝ. It is shown that the mapping a → t(φ(a)) is convex on A. Moreover, the mapping is shown to be nondecreasing if so is φ. Some other similar statements concerning traces and real-valued functions are also obtained.
Traces on JW-Algebras and Enveloping W*-Algebras.
Traces on the cone algebra with asymptotics
Tracial states on crossed products associated with Furstenberg transformations on the 2-torus
Transition probabilities and trace functions for C*-algebras.
Transpositions of UHF algebras.
Travaux de Kadison sur les invariants unitaires
Travaux de N. Higson et G. Kasparov sur la conjecture de Baum-Connes
Triple derivations on von Neumann algebras
It is well known that every derivation of a von Neumann algebra into itself is an inner derivation and that every derivation of a von Neumann algebra into its predual is inner. It is less well known that every triple derivation (defined below) of a von Neumann algebra into itself is an inner triple derivation. We examine to what extent all triple derivations of a von Neumann algebra into its predual are inner. This rarely happens but it comes close. We prove a (triple) cohomological...
Trivial fixed point subalgebras of the rotation algebra.
Trivial noncommutative principal torus bundles
A (smooth) dynamical system with transformation group ⁿ is a triple (A,ⁿ,α), consisting of a unital locally convex algebra A, the n-torus ⁿ and a group homomorphism α: ⁿ → Aut(A), which induces a (smooth) continuous action of ⁿ on A. In this paper we present a new, geometrically oriented approach to the noncommutative geometry of trivial principal ⁿ-bundles based on such dynamical systems, i.e., we call a dynamical system (A,ⁿ,α) a trivial noncommutative principal ⁿ-bundle if each isotypic component...
Trivialization of -algebras with strongly self-absorbing fibres
Suppose is a separable unital -algebra each fibre of which is isomorphic to the same strongly self-absorbing and -injective -algebra . We show that and are isomorphic as -algebras provided the compact Hausdorff space is finite-dimensional. This statement is known not to extend to the infinite-dimensional case.
Truncation and Duality Results for Hopf Image Algebras
Associated to an Hadamard matrix is the spectral measure μ ∈ [0,N] of the corresponding Hopf image algebra, A = C(G) with . We study a certain family of discrete measures , coming from the idempotent state theory of G, which converge in Cesàro limit to μ. Our main result is a duality formula of type , where are the truncations of the spectral measures μ,ν associated to . We also prove, using these truncations , that for any deformed Fourier matrix we have μ = ν.
Twisted crossed products of C*-algebras. II.
Twisted group C*-algebras corresponding to nilpotent discrete groups.
Twisted K-theory of differentiable stacks
Twisted spectral triples and covariant differential calculi
Connes and Moscovici recently studied "twisted" spectral triples (A,H,D) in which the commutators [D,a] are replaced by D∘a - σ(a)∘D, where σ is a second representation of A on H. The aim of this note is to point out that this yields representations of arbitrary covariant differential calculi over Hopf algebras in the sense of Woronowicz. For compact quantum groups, H can be completed to a Hilbert space and the calculus is given by bounded operators. At the end, we discuss an explicit example of...
Two characterizations of automorphisms on B(X)
Let X be an infinite-dimensional Banach space, and let ϕ be a surjective linear map on B(X) with ϕ(I) = I. If ϕ preserves injective operators in both directions then ϕ is an automorphism of the algebra B(X). If X is a Hilbert space, then ϕ is an automorphism of B(X) if and only if it preserves surjective operators in both directions.