Related papers: Fra\"{i}ss\'e theory in operator algebras
We survey the model theory of operator systems and C$^*$-algebras.
We begin the systematic model theoretic study of $\mathrm{C}^*$-algebras using the tools of continuous logic.
In this paper, we present a slightly modified version of Fra\"iss\'e theory which is used in a paper by Christopher J. Eagle, Ilijas Farah, Bradd Hart, Boris Kadets, Vladyslav Kalashnyk and Martino Lupini (arXiv:1411.4066) and another by…
We transcribe a portion of the theory of extensions of C*-algebras to general operator algebras. We also include several new general facts about approximately unital ideals in operator algebras and the C*-algebras which they generate.
We realize the Jiang-Su algebra, all UHF algebras, and the hyperfinite II$_{1}$ factor as Fra\"iss\'e limits of suitable classes of structures. Moreover by means of Fra\"iss\'e theory we provide new examples of AF algebras with strong…
In this article we give a short and informal overview of some aspects of the theory of C*- and von Neumann algebras. We also mention some classical results and applications of these families of operator algebras.
We continue our study of operator algebras with and contractive approximate identities (cais). In earlier papers we have introduced and studied a new notion of positivity in operator algebras, with an eye to extending certain C*-algebraic…
We present a topos-theoretic interpretation of (a categorical generalization of) Fraisse's construction in model theory, with applications to countably categorical theories.
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…
In this exposition, I discuss several developments in the theory of vertex operator algebras, and I include motivation for the definition.
We develop \emph{Fra\"iss\'e theory}, namely the theory of \emph{Fra\"iss\'e classes} and \emph{Fra\"iss\'e limits}, in the context of metric structures. We show that a class of finitely generated structures is Fra\"iss\'e if and only if it…
Examples of operator algebras with involution include the operator $*$-algebras occurring in noncommutative differential geometry studied recently by Mesland, Kaad, Lesch, and others, several classical function algebras, triangular matrix…
We introduce a version of logic for metric structures suitable for applications to C*-algebras and tracial von Neumann algebras. We also prove a purely model-theoretic result to the effect that the theory of a separable metric structure is…
In this master thesis, I discuss how the theory of operator algebras, also called operator theory, can be applied in quantum computer science.
In the setting of modern mathematical logic and model theory, classification theory has been one of the landmark achievements of the field. Likewise, the classification of UHF-algebras and AF-algebras were substantial contributions to the…
We begin a program of generalizing basic elements of the theory of comparison, equivalence, and subequivalence, of elements in C*-algebras, to the setting of more general algebras. In particular, we follow the recent lead of Lin, Ortega,…
We continue our study of operator algebras with contractive approximate identities (cais). In earlier papers we have introduced and studied a new notion of positivity in operator algebras, with an eye to extending certain $C^*$-algebraic…
In this paper, we give a self-contained and quite elementary proof that the class of all dimension drop algebras together with their distinguished faithful traces forms a Fra\"iss\'e class with the Jiang-Su algebra as its limit. We also…
The objectives of this research work which is intimately related to pattern discovery and management are threefold: (i) handle the problem of pattern manipulation by defining operations on patterns, (ii) study the problem of enriching and…
We introduce a Fra\"iss\'e theory for abstract Cuntz semigroups akin to the theory of Fra\"iss\'e categories developed by Kubi\'s. In particular, we show that any (Cuntz) Fra\"iss\'e category has a unique Fra\"iss\'e limit which is both…