Related papers: (No) Wigner Theorem for C*-algebras

We show that several known results about the algebraic K-theory of tensor products of algebras with the C*-algebra of compact operators in Hilbert space remain valid for tensor products with any properly infinite C*-algebra.

Wigner's theorem asserts that an isometric (probability conserving) transformation on a quantum state space must be generated by a Hamiltonian that is Hermitian. It is shown that when the Hermiticity condition on the Hamiltonian is relaxed,…

We show that a tracial state on a unital C*-algebra admits a Haar unitary if and only if it is diffuse, if and only if it does not dominate a tracial functional that factors through a finite-dimensional quotient. It follows that a unital…

We give a notion of branching systems on ultragraphs. From this we build concrete representations of ultragraph C*-algebras on the bounded linear operators of Hilbert spaces. To each branching system of an ultragraph we describe the…

In this article we survey some of the recent goings-on in the classification programme of C$^*$-algebras, following the interesting link found between the Cuntz semigroup and the classical Elliott invariant and the fact that the Elliott…

We show that every infinite-dimensional commutative unital C*-algebra has a Hilbert C*-module admitting no frames. In particular, this shows that Kasparov's stabilization theorem for countably generated Hilbert C*-modules can not be…

C*-algebras are widely used in mathematical physics to represent the observables of physical systems, and are sometimes taken as the starting point for rigorous formulations of quantum mechanics and classical statistical mechanics.…

This paper originates from a naive attempt to establish various non-commutative Fourier theoretic inequalities for an inclusion of simple C*-algebras equipped with a conditional expectation of index-finite type. In this setting, we discuss…

In this paper we analyze states on C*-algebras and their relationship to filter-like structures of projections and positive elements in the unit ball. After developing the basic theory we use this to investigate the Kadison-Singer…

We present a classification theorem for amenable simple stably projectionless C*-algebras with generalized tracial rank one whose $K_0$ vanish on traces which satisfy the Universal Coefficient Theorem. One of them is denoted by ${\cal Z}_0$…

A C*-algebra is n-homogeneous (where n is finite) if every its nonzero irreducible representation acts on an n-dimensional Hilbert space. An elementary proof of Fell's characterization of n-homogeneous C*-algebras (by means of their…

We show that the class of 1-exact operator systems is not uniformly definable by a sequence of types. We use this fact to show that there is no finitary version of Arveson's extension theorem. Next, we show that WEP is equivalent to a…

This expository note presents a constructive proof of Wigner's theorem using only a few basic facts about Hilbert spaces, such as the existence of orthonormal bases and the Fourier decomposition of a vector. Our proof is based on a proof by…

The `Bohrification" program in the foundations of quantum mechanics implements Bohr's doctrine of classical concepts through an interplay between commutative and non-commutative operator algebras. Following a brief conceptual and…

The aim of this work is to complete our program on the quantization of connections on arbitrary principal U(1)-bundles over globally hyperbolic Lorentzian manifolds. In particular, we show that one can assign via a covariant functor to any…

Wigner's theorem asserts that any symmetry of a quantum system is unitary or antiunitary. In this short note we give two proofs based on the geometry of the Fubini-Study metric.

By using C*-correspondences and Cuntz-Pimsner algebras, we associate to every subshift (also called a shift space) $X$ a C*-algebra $O_X$, which is a generalization of the Cuntz-Krieger algebras. We show that $O_X$ is the universal…

In quantum theory, symmetry has to be defined necessarily in terms of the family of unit rays, the state space. The theorem of Wigner asserts that a symmetry so defined at the level of rays can always be lifted into a linear unitary or an…

Naimark's problem asks whether a C*-algebra that has only one irreducible *-representation up to unitary equivalence is isomorphic to the C*-algebra of compact operators on some (not necessarily separable) Hilbert space. This problem has…

We define possibly unsaturated, upper semicontinuous Fell bundles over Hausdorff, locally compact groupoids and establish a universal property for representations of their full section C*-algebras on Hilbert modules over arbitrary…