Related papers: Lecture notes on operator algebras and their appli…
This article introduces classes of normal and unitary operators on smooth Banach spaces, providing extensions of the classical notions of normal and unitary operators from Hilbert spaces to the smooth Banach space setting. The proposed…
In this paper, we investigate the power of nearly purely operational techniques in the study of umbral calculus. We present a concise reconstruction of the theory based on a systematic use of linear operators, with particular attention to…
Resolvents of quasi-linear operators and operator algebras in Banach spaces over the quaternion field are investigated. Spectral theory of unbounded nonlinear operators in quaternion Banach spaces is studied. Strongly continuous semigroups…
Properties of the inverse along an element in rings with an involution, Banach algebras and $C^*$-alegbras will be studied unifying known expressions concerning generalized inverses.
Lecture notes prepared for the EMS--IAMP Spring School ``Symmetries and Measurement in Quantum Field Theory''. This set of lecture notes covers four lectures: 1. Operator Algebras and Quantum Field Theory, 2. Tomita-Takesaki Modular Theory…
We obtain uniqueness theorems for harmonic and subharmonic functions of a new type. They lead to new analytic extension criteria and new conditions for stability of operator semigroups in Banach spaces with Fourier type.
We discuss and develop some connections between analysis on singular spaces and operator algebras, as presented in my sequence of four lectures at the conference "Noncommutative geometry and applications," Frascati, Italy, June 16-21, 2014.…
Lecture notes for an introductory course in elementary particles.
These notes provide an introduction to standard topics on quantum computation and communication for those who already have a basic knowledge of quantum mechanics. The main target audience are professional physicists as well as advanced…
We describe a subclass of the class of normal operators on Banach spaces over non-Archimedean fields (A. N. Kochubei, J. Math. Phys. 51 (2010), article 023526) consisting of operators whose properties resemble those of unitary operators. In…
These lectures introduce the basic ideas and practices of statistical analysis for particle physicists, using a real-world example to illustrate how the abstractions on which statistics is based are translated into practical application.
This is a short review of the algebraic properties of Clifford algebras and spinors. Their use in the description of fundamental physics (elementary particles) is also summarized. Lecture given at the ICCA7 conference, Toulouse (23/05/2005)
We compare two C*-algebras that have been used to study the essential spectrum. This is done by considering a simple second order elliptic differential operator acting in L^2(R^N), which is affiliated with one or both of the algebras…
In this paper we consider shift operators, self-adjoint, unitary and normal operators on the standard module over a unital C*-algebra A. We define various generalized spectra in A of these operators, give description of such spectra of…
Some ideas about phenomenological applications of quantum algebras to physics are reviewed. We examine in particular some applications of the algebras $U_ q (su_2)$ and $U_{qp}({\rm u}_2)$ to various dynamical systems and to atomic and…
We give a necessary and sufficient condition for amenability of the Banach algebra of approximable operators on a Banach space. We further investigate the relationship between amenability of this algebra and factorization of operators,…
Classical Banach principle is an essential tool for the investigation of the ergodic properties of Cesaro subsequences. The aim of this work is to extend Banach principle to the case of the stochastic convergence in the operator algebras.…
This paper introduces the notion of Rota-Baxter $C^{\ast}$-algebras. Here a Rota-Baxter $C^{\ast}$-algebra is a $C^{\ast}$-algebra with a Rota-Baxter operator. Symmetric Rota-Baxter operators, as special cases of Rota-Baxter operators on…
Let $A,$ $T$ and $B$ be bounded linear operators on a Banach space. This paper is concerned mainly with finding some necessary and sufficient conditions for convergence in operator norm of the sequences $\left\{ A^{n}TB^{n}\right\} $ and…
In this paper, we study the matrix multiplication operators on Banach function spaces and discuss their applications in semigroups for solving the abstract Cauchy problem.