Related papers: Operator systems for tolerance relations on finite…
We answer, by counterexample, several open questions concerning algebras of operators on a Hilbert space. The answers add further weight to the thesis that, for many purposes, such algebras ought to be studied in the framework of operator…
Complex systems are composed of a large number of simple components connected to each other in the form of a network. It is shown that, for some network configurations, the equivalent dynamic behavior of the system is governed by an…
We define and investigate properties of universal operator algebras of directed graphs. Results include free products decomposition and continuity of the construction with respect to direct limits. Lastly we prove some K-theoretic results…
A Dirichlet operator algebra is a nonself-adjoint operator algebra $\mathcal{A}$ with the property that $\mathcal{A} + \mathcal{A}^*$ is norm-dense in the C$^*$-envelope of $\mathcal{A}.$ We show that, under certain restrictions,…
The representation of the resolvent as an integral operator, the $m$ function, and the associated spectral representation are fundamental topics in the spectral theory of self-adjoint ordinary differential operators. Versions of these are…
Motivated by a recent conjecture of Misumi and Yumoto relating the number of zero modes of lattice Dirac operators to the sum of the Betti numbers of the underlying spacetime manifold, we study formal naive Dirac operators on a class of…
In this paper we study the subdifferential set of an operator. We give possible relation of the subdifferential set of an operator to that of its value, at a point where the operator attains its norm.
We introduce order conserving embeddings as a more general form of order preserving embeddings between finite dimensional nest algebras. The structure of these embeddings is determined, in terms of order indecomposable decompositions, and…
This article is devoted to the investigation of $B^*$-algebras, dual and annihilator ultranormed algebras. Their structure is studied in the paper. Extensions of algebras and fields are considered and using them core radicals and radicals…
We introduce two mirror constructions of Vertex Operator Algebras associated to special boundary conditions in 3d N=4 gauge theories. We conjecture various relations between these boundary VOA's and properties of the (topologically twisted)…
The paper deals with a construction of a separating system of rational invariants for finite dimensional generic algebras. In the process of dealing an approach to a rough classification of finite dimensional algebras is offered by…
We study the design of graph filters to implement arbitrary linear transformations between graph signals. Graph filters can be represented by matrix polynomials of the graph-shift operator, which captures the structure of the graph and is…
For orthoposets we introduce a binary relation Delta and a binary operator d(x,y) which are generalizations of the binary relation C and the commutator c(x,y), respectively, known for orthomodular lattices. We characterize orthomodular…
This paper studies infinite graphs produced from a natural unfolding operation applied to finite graphs. Graphs produced via such operations are of finite degree and automatic over the unary alphabet (that is, they can be described by…
Graph-based signal processing techniques have become essential for handling data in non-Euclidean spaces. However, there is a growing awareness that these graph models might need to be expanded into `higher-order' domains to effectively…
We present an intuitive formalism for implementing cellular automata on arbitrary topologies. By that means, we identify a symmetry operation in the class of elementary cellular automata. Moreover, we determine the subset of topologically…
In this paper, we introduce a new operator, $\mathcal{S}$, which is closely related to the restriction problem for spheres in $\mathbb{F}_q^d$, the $d$-dimensional vector space over the finite field $\mathbb{F}_q$ with $q$ elements. The…
An operator system $\cl S$ with unit $e$, can be viewed as an Archimedean order unit space $(\cl S,\cl S^+,e)$. Using this Archimedean order unit space, for a fixed $k\in \bb N$ we construct a super k-minimal operator system OMIN$_k(\cl S)$…
Learning dynamical systems through operator-theoretic representations provides a powerful framework for analyzing complex dynamics, as spectral quantities such as eigenvalues and invariant structures encode characteristic time scales and…
We study the properties of shifted vertex operator algebras, which are vertex algebras derived from a given theory by shifting the conformal vector. In this way, we are able to exhibit large numbers of vertex operator algebras which are…