Related papers: $C^*$-algebra Net: A New Approach Generalizing Neu…

The universal C*-algebra generated by n projections has been described. As an immediate corollary one obtains structure theorem for a pair of projections and the solution to an associated index problem. This puts the study of a pair of…

This is the final one in the series of papers where we introduce and study the $C^*$-algebras associated with topological graphs. In this paper, we get a sufficient condition on topological graphs so that the associated $C^*$-algebras are…

Certain $*$-semigroups are associated with the universal $C^*$-algebra generated by a partial isometry, which is itself the universal $C^*$-algebra of a $*$-semigroup. A fundamental role for a $*$-structure on a semigroup is emphasized, and…

To a large class of graphs of groups we associate a C*-algebra universal for generators and relations. We show that this C*-algebra is stably isomorphic to the crossed product induced from the action of the fundamental group of the graph of…

Let $n$ be a natural number. Recall that a C*-algebra is said to be $n$-subhomogeneous if all its irreducible representations have dimension at most $n$. In this short note, we give various approximation properties characterising…

We extend applications of Furstenberg boundary theory to the study of $C^*$-algebras associated to minimal actions $\Gamma\!\curvearrowright\! X$ of discrete groups $\Gamma$ on locally compact spaces $X$. We introduce boundary maps on…

We study a family of C*-algebras generalizing both Katsura algebras and certain algebras introduced by Nekrashevych in terms of self-similar groups.

While a real-world research program in mathematics may be guided by a motivating question, the process of mathematical discovery is typically open-ended. Ideally, exploration needed to answer the original question will reveal new…

In the given article the notion of infinite norm decomposition of a C$^*$-algebra is investigated. The norm decomposition is some generalization of Peirce decomposition. It is proved that the infinite norm decomposition of any C$^*$-algebra…

Graph neural networks (GNNs) are the most widely adopted model in graph-structured data oriented learning and representation. Despite their extraordinary success in real-world applications, understanding their working mechanism by theory is…

We define and examine sequentially split $*$-homomorphisms between $\mathrm{C}^*$-algebras and $\mathrm{C}^*$-dynamical systems. For a $*$-homomorphism, the property of being sequentially split can be regarded as an approximate weakening of…

A Banach space characterization of simple real or complex $C^*$-algebras is given which even characterizes the underlying field. As an application, it is shown that if $\mathfrak A_1$ and $\mathfrak A_2$ are Birkhoff-James isomorphic simple…

We give a definition of partition C*-algebras: To any partition of a finite set, we assign algebraic relations for a matrix of generators of a universal C*-algebra. We then prove how certain relations may be deduced from others and we…

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…

In a recent paper of the first author and Kashyap, a new class of modules over dual operator algebras is introduced. These generalize the W*-modules (that is, Hilbert C*-modules over a von Neumann algebra which satisfy an analogue of the…

We investigate how a C*-algebra could consist of functions on a noncommutative set: a discretization of a C*-algebra $A$ is a $*$-homomorphism $A \to M$ that factors through the canonical inclusion $C(X) \subseteq \ell^\infty(X)$ when…

A pro-C^*-algebra is a (projective) limit of C^*-algebras in the category of topological *-algebras. From the perspective of non-commutative geometry, pro-C^*-algebras can be seen as non-commutative k-spaces. An element of a pro-C^*-algebra…

We give a classification result for a certain class of $C^{*}$-algebras $\mathfrak{A}$ over a finite topological space $X$ in which there exists an open set $U$ of $X$ such that $U$ separates the finite and infinite subquotients of…

We consider inductive systems of C*-algebras with completely positive contractive connecting maps. We define a condition, called C*-encoding, which is sufficient for the limit of the system to be completely order isomorphic to a C*-algebra…

We consider problems associated with the computation of spectra of self-adjoint operators in terms of the eigenvalue distributions of their n x n sections. Under rather general circumstances, we show how these eigenvalues accumulate near…