Related papers: An Algebraic Study of Averaging Operators
An averaging operator on an associative algebra $A$ is an algebraic abstraction of the time average operator on the space of real-valued functions defined in time-space. In this paper, we consider relative averaging operators on a bimodule…
This paper considers averaging operators on various algebraic structures and studies the induced structures. We first introduce the notion of an averaging operator on a group $G$ and show that it induces a rack structure. Moreover, the…
In this paper, we study averaging operators from an algebraic and combinatorial point of view. We first construct free averaging algebras in terms of a class of bracketed words called averaging words. We next apply this construction to…
Rota-Baxter operators on groups were studied quite recently. Motivated mainly by the fact that weight zero Rota-Baxter operators and averaging operators are Koszul dual to each other, we propose the concepts of averaging group and averaging…
In recent years, averaging operators on Lie algebras (also called embedding tensors in the physics literature) and associated tensor hierarchies form an efficient tool for constructing supergravity and higher gauge theories. A Lie algebra…
Let E be an operator algebra on a Hilbert space with finite-dimensional generated C*-algebra. A classification is given of the locally finite algebras and the operator algebras obtained as limits of direct sums of matrix algebras over E…
In this paper, we introduce the concepts of endomorphism operator, left averaging operator, differential operator and Rota-Baxter Operator, and we construct examples of these linear maps on associative algebras with a left identity, a…
We introduce the notion of a Lie algebroid structure on an affine bundle whose base manifold is fibred over the real numbers. It is argued that this is the framework which one needs for coming to a time-dependent generalization of the…
The operator algebra is introduced based on the framework of logarithmic representation of infinitesimal generators. In conclusion a set of generally-unbounded infinitesimal generators is characterized as a module over the Banach algebra.
Let X be a Banach space over field F (R or C). Denote by B(X) the set of all bounded linear operators on X and by F(X) the set of all finite rank operators on X. A subalgebra A of B(X) is called a standard operator algebra if A contain…
We introduce the notion of relative averaging operators on Hom-associative algebras with a representation. Relative averaging operators are twisted generalizations of relative averaging operators on associative algebras. We give two…
In this paper, we first introduce the notion of a (relative) averaging operator of any nonzero weight $\lambda$. We show that such operators are intimately related to triassociative algebras introduced by Loday and Ronco. Next, we construct…
The Leibniz bracket of an operator on a (graded) algebra is defined and some of its properties are studied. A basic theorem relating the Leibniz bracket of the commutator of two operators to the Leibniz bracket of them, is obtained. Under…
We use the Fock semicrossed product to define an operator algebra associated to a module over an integral domain. We consider the $C^*$-envelope of the semicrossed product, and then consider properties of these algebras as models for…
By considering generalized logarithm and exponential functions used in nonextensive statistics, the four usual algebraic operators : addition, subtraction, product and division, are generalized. The properties of the generalized operators…
This is an introduction to the algebras $A\subset B(H)$ that the linear operators $T:H\to H$ can form, once a complex Hilbert space $H$ is given. Motivated by quantum mechanics, we are mainly interested in the von Neumann algebras, which…
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…
In this paper we consider the $f$-orthomorphisms and $f$-linear operators on the order dual of an $f$-algebra. In particular, when the $f$-algebra has the factorization property (not necessarily unital), we prove that the orthomorphisms,…
Operator algebras generated by partial isometries and their adjoints form the basis for some of the most well studied classes of C*-algebras. The primary object of this paper is the norm-closed operator algebra generated by a left…
In this paper, we study the structure and representation of a $6A$-algebra which is a vertex operator algebra generated by two Ising vectors $e,f$ with inner product $\left\langle e,f\right\rangle =\frac{5}{2^{10}}.$ In particular, we prove…