Related papers: Peripheral Poisson Boundary on Full Fock space
For locally compact groups G and H let A(G) denote the Fourier algebra of G and B(H) the Fourier-Stieltjes algebra of H. Any continuous piecewise affine map alpha:Y -> G (where Y is an element of the open coset ring of H) induces a…
The generalized state space of a commutative C*-algebra, denoted S_H(C(X)), is the set of positive unital maps from C(X) to the algebra B(H) of bounded linear operators on a Hilbert space H. C*-convexity is one of several non-commutative…
This is an introduction to the algebras $A\subset B(H)$ that the linear operators $T:H\to H$ can form, once a complex Hilbert space $H$ is given. Motivated by quantum mechanics, we are mainly interested in the von Neumann algebras, which…
The goal of this paper is to give an explicit construction of the Fock spaces of the parafermion and the paraboson algebra, for an infinite set of generators. This is equivalent to constructing certain unitary irreducible lowest weight…
The set of normalizers between von Neumann (or, more generally, reflexive) algebras A and B, (that is, the set of all operators x such that xAx* is a subset of B and x*Bx is a subset of A) possesses `local linear structure': it is a union…
The Poisson boundary of a group G with a probability measure \mu is the space of ergodic components of the time shift in the path space of the associated random walk. Via a generalization of the classical Poisson formula it gives an…
We study the closure of the unitary orbit of a given point in the non-commutative Choquet boundary of a unital operator space with respect to the topology of pointwise norm convergence. This may be described more extensively as the…
Assuming a unitarily invariant norm $|||\cdot|||$ is given on a two-sided ideal of bounded linear operators acting on a separable Hilbert space, it induces some unitarily invariant norms $|||\cdot|||$ on matrix algebras $\mathcal{M}_n$ for…
Let $H$ be an infinite dimensional separable Hilbert space, $B(H)$ the $C^*$-algebra of all bounded linear operators on $H,$ $U(B(H))$ the unitary group of $B(H)$ and ${\cal K}\subset B(H)$ the ideal of compact operators. Let $G$ be a…
We identify and characterize unital completely positive (UCP) maps on finite dimensional $C^*$-algebras for which the Choi-Effros product extended to the space generated by peripheral eigenvectors matches with the original product. We…
The group of affine transformations with rational coefficients acts naturally on the real line, but also on the $p$-adic fields. The aim of this note is to show that, for random walks whose laws have a finite first moment, all these actions…
In his work on crystal bases \cite{Kas}, Kashiwara introduced a certain degeneration of the quantized universal enveloping algebra of a semi-simple Lie algebra $\mathfrak g$, which he called a quantum boson algebra. In this paper, we…
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…
We prove that a unital completely positive map between finite-dimensional C*-algebras is a homomorphism if and only if it is completely entropy-nonincreasing, where the relevant notion of entropy is a variant of von Neumann entropy. This…
It is shown that the new Poisson brackets proposed in Part I of this work (J. Math. Phys. 34, 5747(hep-th/9305133)) arise naturally in an extension of the formal variational calculus incorporating divergences. The linear spaces of local…
The order relation on the set of completely n-positive linear maps from a pro-C*-algebra A to L(H), the C*-algebra of bounded linear operators on a Hilbert space H, is characterized in terms of the representation associated with each…
The aim of this note is to describe the Poisson boundary of the group of invertible triangular matrices with coefficients in a number field. It generalizes to any dimension and to any number field a result of Brofferio concerning the…
The notion of bounded element of C*-inductive locally convex spaces (or C*-inductive partial *-algebras) is introduced and discussed in two ways: the first one takes into account the inductive structure provided by certain families of…
If $\mathfrak{g}$ is a Lie algebra then the semi-centre of the Poisson algebra $S(\mathfrak{g})$ is the subalgebra generated by ad$(\mathfrak{g})$-eigenvectors. In this paper we abstract this definition to the context of integral Poisson…
The common structure of the space of pure states $P$ of a classical or a quantum mechanical system is that of a Poisson space with a transition probability. This is a topological space equipped with a Poisson structure, as well as with a…