Related papers: Symmetric states for $C^*$-Fermi systems I: De Fin…

We study the C*-algebras of Fell bundles. In particular, we prove the analogue of Renault's disintegration theorem for groupoids. As in the groupoid case, this result is the key step in proving a deep equivalence theorem for the C*-algebras…

In this paper, we introduce a C*-algebra associated to any substitution (via its Bratteli diagram model). We show that this C*-algebra contains the partial crossed product C*-algebra of the corresponding Bratteli-Vershik system and show…

In this paper we study the structure of the $C^*$-algebra, generated by the representation of the paths semigroup on a partially ordered set (poset) and get the net of isomorphic $C^*$-algebras over this poset. We construct the extensions…

Let (G,P) be a quasi-lattice ordered group and let X be a compactly aligned product system over P of Hilbert bimodules. Under mild hypotheses we associate to X a C*-algebra which we call the Cuntz-Nica-Pimsner algebra of X. Our construction…

The quantum de Finetti theorem asserts that the k-body density matrices of a N-body bosonic state approach a convex combination of Hartree states (pure tensor powers) when N is large and k fixed. In this note we review a construction due to…

We present a general approach to a modular frame theory in C*-algebras and Hilbert C*-modules. The investigations rely on the idea of geometric dilation to standard Hilbert C*-modules over unital C*-algebras that possess orthonormal Hilbert…

We describe a class of $C^*$-algebras which simultaneously generalise the ultragraph algebras of Tomforde and the shift space $C^*$-algebras of Matsumoto. In doing so we shed some new light on the different $C^*$-algebras that may be…

We consider a product system over the multiplicative semigroup N^x of Hilbert bimodules which is implicit in work of S. Yamashita and of the second named author. We prove directly, using universal properties, that the associated…

The set of spreadabl estates on an infinite non-commutive torus \mathbb{A}_{\mathbb{Z}_\alpha} is determined for all values of the deformation parameter {\alpha}. If {\alpha} is irrational, the canonical trace is the only spreadable 2{\pi}…

We discuss a synchronization property for subshifts, that we call $\lambda$-synchronization. Under an irreducibility assumption we associate to a $\lambda$-synchronizing subshift a simple and purely infinite $C^*$-algebra.

Different (fibrewise) amalgamated products of continuous C*-bundles have been studied over the last years, one of the main question being to know when these amalgamated products are continuous C*-bundles. In order to gather these approaches…

A Hilbert $C^*$-quad module of finite type has a multi structure of Hilbert $C^*$-bimodules with two finite bases. We will construct a $C^*$-algebra from a Hilbert $C^*$-quad module of finite type and prove its universality subject to…

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 review the notions of a multiplier category and the $W^{*}$-envelope of a $C^{*}$-category. We then consider the notion of an orthogonal sum of a (possibly infinite) family of objects in a $C^{*}$-category. Furthermore, we construct…

We define the notion of a $\Lambda$-system of $C^*$-correspondences associated to a higher-rank graph $\Lambda$. Roughly speaking, such a system assigns to each vertex of $\Lambda$ a $C^*$-algebra, and to each path in $\Lambda$ a…

We introduce the notion of confined subalgebras in the context of the group von Neumann algebra. We also define Uniformly Recurrent States -- an operator-algebraic analog of Uniformly Recurrent Subgroups. Using this framework, we show that…

A classic and fundamental result about the decomposition of random sequences into a mixture of simpler ones is de Finetti's Theorem. In its original form it applies to infinite 0-1 valued exchangeable sequences. Later it was extended and…

We show that every continuous product system of correspondences over a unital C*-algebra occurs as the product system of a strictly continuous E_0-semigroup.

The extension problem asks whether positive semi-definite functions on a symmetric unital subset of a discrete group can be extended to positive semi-definite functions on the whole group. It has been known at least since the work of Rudin…

We present a unitary approach to the construction of representations and intertwining operators. We apply it to the $C^*$-algebras, groups, Gabor type unitary systems and wavelets. We give an application of our method to the theory of…