Related papers: $C^*$-algebras: The (Quantum) Path Less Traveled

This paper gives a first step toward extending the theory of Fourier-Stieltjes algebras from groups to groupoids. If G is a locally compact (second countable) groupoid, we show that B(G), the linear span of the Borel positive definite…

We propose an abstract framework of a kind of representation theory for $C^*$-flows, i.e., $C^*$-algebras equipped with one-parameter automorphism groups, as a proper generalization of Olshanski's formalism of unitary representation theory…

We show how the proof of the Grothendieck Theorem for jointly completely bounded bilinear forms on C*-algebras by Haagerup and Musat can be modified in such a way that the method of proof is essentially C*-algebraic. To this purpose, we use…

For a space $X$ denote by $C_b(X)$ the Banach algebra of all continuous bounded scalar-valued functions on $X$ and denote by $C_0(X)$ the set of all elements in $C_b(X)$ which vanish at infinity. We prove that certain Banach subalgebras $H$…

This work provides a generalization of the Gelfand duality to the context of noncommutative locally $C^*$ algebras. Using a reformulation of a theorem proven by Dauns and Hofmann in the 60's we show that every locally $C^*$ algebra can be…

In this paper we show that the universal C*-algebra satisfying the Cuntz-Li relations is generated by an inverse semigroup of partial isometries. We apply Exel's theory of tight representations to this inverse semigroup. We identify the…

We extend the definition of the bivariant $K$-theory $kk^{ban}$ from plain Banach algebras to Banach algebras equipped with an action of a locally compact Hausdorff group $G$. We also define a natural transformation from Lafforgue's theory…

A novel C*-algebraic framework is presented for relativistic quantum field theories, fixed by a Lagrangean. It combines the postulates of local quantum physics, encoded in the Haag-Kastler axioms, with insights gained in the perturbative…

A C*-algebra formulation of Quantum Mechanics is derived from purely operational axioms in which the primary role is played by the "transformations" that the system undergoes in the course of an "experiment". The notion of the {\em adjoint}…

We write arbitrary separable nuclear C*-algebras as limits of inductive systems of finite-dimensional C*-algebras with completely positive connecting maps. The characteristic feature of such CPC*-systems is that the maps become more and…

We introduce a non-commutative generalization of the notion of (approximately proper) equivalence relation and propose the construction of a "quotient space". We then consider certain one-parameter groups of automorphisms of the resulting…

We introduce a new class of operator algebras -- tracially complete C*-algebras -- as a vehicle for transferring ideas and results between C*-algebras and their tracial von Neumann algebra completions. We obtain structure and classification…

We use the crystallised $C^*$-algebra $C(SU_{q}(2))$ at $q=0$ to obtain a unitary that gives an approximate equivalence involving the GNS representation on the $L^{2}$ space of the Haar state of the quantum $SU(2)$ group and the direct…

We extend the $C^*$-algebraic approach to interacting quantum field theory, proposed recently by Detlev Buchholz and one of us (KF) to Fermi fields. The crucial feature of our approach is the use of auxiliary Grassmann variables in a…

We define a categorical framework in which we build a systematic construction that provides generic invariants for C*-algebras. The benefit is significant as we show that any invariant arising this way automatically enjoys nice properties…

We consider the $C^*$-algebra generated by finitely many annihilation operators acting on the weakly monotone Fock space, and we call it weakly monotone $C^*$-algebra. We give an abstract representation for this algebra, showing that it is…

The well-behaved representations of the coordinate algebra of a 2-dimensional quantum complex plane are classified and a C*-algebra is defined which can be viewed as the algebra of continuous functions on the 2-dimensional quantum complex…

In this paper, we apply the theory of inverse semigroups to the $C^{*}$-algebra $U[\mathbb{Z}]$ considered in \cite{Cuntz}. We show that the $C^{*}$-algebra $U[\mathbb{Z}]$ is generated by an inverse semigroup of partial isometries. We…

In this paper, a new invariant was built towards the classification of separable C*-algebras of real rank zero, which we call latticed total K-theory. A classification theorem is given in terms of such an invariant for a large class of…

Using Cuntz semigroup techniques, we characterize when limit traces are dense in the space of all traces on a free ultrapower of a C*-algebra. More generally, we consider density of limit quasitraces on ultraproducts of C*-algebras. Quite…