Related papers: Stinespring's construction as an adjunction
This paper is about the reduced group C*-algebras of real reductive groups, and about Hilbert C*-modules over these C*-algebras. We shall do three things. First we shall apply theorems from the tempered representation theory of reductive…
We show that pure strongly continuous semigroups of adjointable isometries on a Hilbert C*-module are standard right shifts. By counter examples, we illustrate that the analogy of this result with the classical result on Hilbert spaces by…
Motivated by advances in categorical probability, we introduce non-commutative almost everywhere (a.e.) equivalence and disintegrations in the setting of C*-algebras. We show that C*-algebras (resp. W*-algebras) and a.e. equivalence classes…
We establish a finite-dimensional version of the Arveson-Stinespring dilation theorem for unital completely positive maps on operator systems. This result can be seen as a general principle to deduce finite-dimensional dilation theorems…
In this paper, motivated by the Berger, Coburn and Lebow and Bercovici, Douglas and Foias theory for tuples of commuting isometries, we study analytic representations and joint invariant subspaces of a class of commuting $n$-isometries and…
An operator *-algebra is a non-selfadjoint operator algebra with completely isometric involution. We show that any operator *-algebra admits a faithful representation on a Hilbert space in such a way that the involution coincides with the…
The reticulation of an algebra $A$ is a bounded distributive lattice ${\cal L}(A)$ whose prime spectrum of filters or ideals is homeomorphic to the prime spectrum of congruences of $A$, endowed with the Stone topologies. We have obtained a…
A densely-defined symmetric linear map from/to a real Hilbert space extends to a self-adjoint map. Extension is expressed via Riesz representation. For a case including Friedrichs extension of a strongly monotone map, self-adjoint extension…
Let $M$ be a von Neumann algebra with a faithful normal finite trace $t$, and $H^\infty$ be a finite, maximal, subdiagonal of $M$. Fundamental theorems on conjugate functions for weak* Dirichlet algebras are shown to be a bounded linear map…
Consider a unital C*-algebra A, a von Neumann algebra M, a unital sub-C*-algebra C of A and a unital *-homomorphism $\pi$ from C to M. Let u: A --> M be a decomposable map (i.e. a linear combination of completely positive maps) which is a…
We consider perturbations of dynamical semigroups on the algebra of all bounded operators in a Hilbert space generated by covariant completely positive measures on the semi-axis. The construction is based upon unbounded linear perturbations…
We prove that every surjective unital linear mapping which preserves invertible elements from a Banach algebra onto a C*-algebra carrying a faithful tracial state is a Jordan homomorphism thus generalising Aupetit's 1998 result for finite…
It is proved that that every nilpotent contraction in a quotient C*-algebra can be lifted to a nilpotent contraction. As a consequence we get that the universal C*-algebra generated by a nilpotent contraction is projective. This answers the…
In this paper, we consider the gauge-invariant ideal structure of a $C^*$-algebra $C^*(E,\mathcal{L},\mathcal{B})$ associated to a set-finite, receiver set-finite and weakly left-resolving labelled space $(E,\mathcal{L},\mathcal{B})$, where…
We prove that unital graph C*-algebras often admit a convenient decomposition into amalgamated free products. We use this to give a complete characterization of when a unital graph C*-algebra is residually finite-dimensional and when it is…
We consider a version of a famous open problem formulated by Kadison, asking whether bounded representations of operator algebras are automatically completely bounded. We investigate this question in the context of amenable operator…
Let E be a row-finite directed graph. We prove that there exists a C*-algebra C*_{min}(E) with the following co-universal property: given any C*-algebra B generated by a Toeplitz-Cuntz-Krieger E-family in which all the vertex projections…
The Kadison-Singer problem asks: does every pure state on the diagonal sublgebra of the C*-algebra of bounded operators on a separable infinite dimensional Hilbert space admit a unique extension? A yes answer is equivalent to several open…
We introduce and analyse the structure of C*-algebras arising from ideals in right tensor C*-precategories, which naturally generalize both relative Cuntz-Pimsner and Doplicher-Roberts algebras. We establish an explicit intrinsic…
It is proved that every separable $C^*$-algebra of real rank zero contains an AF-sub-$C^*$-algebra such that the inclusion mapping induces an isomorphism of the ideal lattices of the two $C^*$-algebras and such that every projection in a…