Related papers: Lecture notes on operator algebras and their appli…
A short introduction to the mathematical methods and technics of differential algebras and modules adapted to the problems of mathematical and theoretical physics is presented.
Several basic properties of the Drazin spectrum in Banach algebras will be studied. As an application, some results on meromorphic Banach space operators will be obtained.
We survey the model theory of operator systems and C$^*$-algebras.
Operator learning refers to the application of ideas from machine learning to approximate (typically nonlinear) operators mapping between Banach spaces of functions. Such operators often arise from physical models expressed in terms of…
This note recapitulates and expands the contents of a tutorial on the mathematical theory of algebraic effects and handlers which I gave at the Dagstuhl seminar 18172 "Algebraic effect handlers go mainstream". It is targeted roughly at the…
Vertex operator algebras are mathematically rigorous objects corresponding to chiral algebras in conformal field theory. Operads are mathematical devices to describe operations, that is, $n$-ary operations for all $n$ greater than or equal…
The paper contains Boas-type formulas for trajectories of one-parameter groups of operators in Banach spaces. The results are illustrated using one-parameter groups of operators which appear in representations of Lie groups.
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…
Remarks are given to the structure of physical states in 2D gravity coupled to $C\leq 1$ matter. The operator algebra of the discrete state operators is calculated for the theory with non-vanishing cosmological constant.
This book treats: - spectral theory of Banach *-algebras, - basic representation theory of normed *-algebras, - spectral theory of representations of commutative *-algebras. A novel feature of the book is the construction of the enveloping…
These are lecture notes for a 1-semester undergraduate course (in computer science, mathematics, physics, engineering, chemistry or biology) in applied categorical meta-language. The only necessary background for comprehensive reading of…
In this project, we will develop the theory of Banach algebras and prove two celebrated theorems, the Gelfand representation theorem and the GKZ theorem. We will then proceed to develop the theory of $C^*$-algebras and prove the…
In this paper we introduce and study a new class of operators related to norm bounded sets on Banach Lattice and which brings together several classical classes of operators (as o-weakly compact operators, b-weakly compact operators,…
We present geometric characterizations of the partial isometries, unitaries, and invertible operators in C*-algebras and von Neumann algebras.
These lecture notes are an informal introduction to the theory of computational complexity and its links to quantum computing and statistical mechanics.
These notes were compiled as lecture notes for a course developed and taught at the University of the Southern California. They should be accessible to a typical engineering graduate student with a strong background in Applied Mathematics.…
We consider weakly closed transitive algebras of operators containing non-zero compact operators in real Banach spaces (Lomonosov algebras). It is shown that they are naturally divided in three classes: the algebras of real, complex and…
Operator systems are the unital self-adjoint subspaces of the bounded operators on a Hilbert space. Complex operator systems are an important category containing the C*-algebras and von Neumann algebras, which is increasingly of interest in…
We discuss certain ternary algebraic structures appearing more or less naturally in various domains of theoretical and mathematical physics. Far from being exhaustive, this article is intended above all to draw attention to these algebras,…
In this thesis we explore the the possibility of characterising C* algebras by their (non-isometric) Banach algebra structure alone. We introduce a property of Banach algebras, the Total Reduction Property, and conjecture that a Banach…