Related papers: On Generalized Powers of Operators
The present paper is a sequel to our paper "Metric characterization of isometries and of unital operator spaces and systems". We characterize certain common objects in the theory of operator spaces (unitaries, unital operator spaces,…
Recently, P\'{a}lfia introduced a generalized Karcher mean as a solution of an operator equation. In this article, we present several relations for this new mean. In particular, we investigate the behavior of this generalized mean when…
Square of a posinormal operator is not necessarily posinormal$.$ But (i) powers of quasiposinormal operators are quasiposinormal and, under closed ranges assumption, powers of (ii) posinormal operators are posinormal, (iii) of operators…
The paper deals with generalized positive linear operators based on P\'olya-Eggenberger distribution(PED) as well as inverse P\'olya-Eggenberger distribution(IPED). Initially, we give the moments by using Stirling numbers of second kind and…
Given an automorphism and an anti-automorphism of a semigroup of a Geometric Algebra, then for each element of the semigroup a (generalized) projection operator exists that is defined on the entire Geometric Algebra. A single fundamental…
Given a polynomial $f$ with coefficients in a field of prime characteristic $p$, it is known that there exists a differential operator that raises $1/f$ to its $p$th power. We first discuss a relation between the `level' of this…
In this letter we make a brief review of some basic properties (the matrix elements, the trace, the Glauber formula) of coherent operators and study the corresponding ones for generalized coherent operators based on Lie algebra su(1,1). We…
A common theme in mathematics is to define generalized solutions to deal with problems that potentially do not have solutions. A classical example is the introduction of least squares solutions via the normal equations associated with a…
In this paper we explore the theory of fractional powers of non-negative (and not necessarily self-adjoint) operators and its amazing relationship with the Chebyshev polynomials of the second kind to obtain results of existence, regularity…
The generalized divided differences are introduced. They are applied to investigate some properties characterizing generalized higher-order convexity. Among others some support-type property is proved.
We introduce and study the generalized Wigner operator. By definition, such an operator transforms the Wigner wave function into a local relativistic field corresponding to an irreducible representation of the Poincar\'e group by extended…
A generalization of Powers-St$\o$rmer's inequality for operator monotone functions on $[0, +\infty)$ and for positive linear functional on general $C^*$-algebras will be proved. It also will be shown that the generalized Powers-St$\o$rmer…
We investigate some types of composition operators, linear and not, and conditions for some spaces to be mapped into themselves and for the operators to satisfy some good properties.
We present an abstract result that characterizes the coincidence of certain classes of linear operators with the class of Cohen strongly summing linear operators. Our argument is extended to multilinear operators and, as a consequence, we…
In the present article, we propose the new class positive linear operators, which discrete type depending on a real parameters. These operators are similar to Jain operators but its approximation properties are different then Jain…
The purpose of this paper is to give a characterisation of divided power algebras over a reduced operad. Such a characterisation is given in terms of polynomial operations, following the classical example of divided power algebras. We…
Starting from a description of various generalized function algebras based on sequence spaces, we develop the general framework for considering linear problems with singular coefficients or non linear problems. Therefore, we prove…
This is a straightforward introduction to the properties of polynomials in many variables that do not vanish in the open upper half plane. Such polynomials generalize many of the well-known properties of polynomials with all real roots.
In this paper we discuss generalized group, provides some interesting examples. Further we introduce a generalized module as a module like structure obtained from a generalized group and discuss some of its properties and we also describes…
We investigate the combinatorics of the general formulas for the powers of the operator $h \partial^k$, where $h$ is a central element of a ring and $\partial$ is a differential operator. This generalizes previous work on the powers of…