A complete characterization of smoothness in the space of bounded linear operators [PDF]
We completely characterize smoothness of bounded linear operators between infinite dimensional real normed linear spaces, probably for the very first time, by applying the concepts of Birkhoff-James orthogonality and semi-inner-products in normed linear ...
D. Sain, K. Paul, A. Mal, A. Ray
semanticscholar +1 more source
Estimates for the differences of positive linear operators and their derivatives [PDF]
The present paper deals with the estimate of the differences of certain positive linear operators and their derivatives. Oxur approach involves operators defined on bounded intervals, as Bernstein operators, Kantorovich operators, genuine Bernstein ...
A. Acu, I. Raşa
semanticscholar +1 more source
Structure theorems for linear and non-linear differential operators admitting invariant polynomial subspaces [PDF]
In this paper we derive structure theorems that characterize the spaces of linear and non-linear differential operators that preserve finite dimensional subspaces generated by polynomials in one or several variables.
Gomez-Ullate, David+2 more
core +4 more sources
Optical complex media as universal reconfigurable linear operators [PDF]
Performing linear operations using optical devices is a crucial building block in many fields ranging from telecommunication to optical analogue computation and machine learning.
Maxime W. Matthès+4 more
semanticscholar +1 more source
Continuity of Linear Operators Commuting with Continuous Linear Operators [PDF]
1. Introduction. In [6] and [8] we showed that centralisers (that is operators commuting with multiplication) on certain Banach algebras are necessarily continuous. In the present paper we consider whether an operator on a Banach space commuting with a continuous or a closed operator must itself be continuous.
openaire +2 more sources
Extremal Non-Compactness of Composition Operators with Linear Fractional Symbol [PDF]
We realize norms of most composition operators acting on the Hardy space with linear fractional symbol as roots of hypergeometric functions. This realization leads to simple necessary and sufficient conditions on the symbol to exhibit extremal non ...
Basor, Estelle L., Retsek, Dylan Q.
core +2 more sources
An inequality for imaginary parts of eigenvalues of non-compact operators with Hilbert-Schmidt Hermitian components [PDF]
Let \(A\) be a bounded linear operator in a complex separable Hilbert space, \(A^*\) be its adjoint one and \(A_I:=(A-A^*)/(2i)\). Assuming that \(A_I\) is a Hilbert-Schmidt operator, we investigate perturbations of the imaginary parts of the ...
Michael Gil'
doaj +1 more source
Linear differential operators on contact manifolds [PDF]
We consider differential operators between sections of arbitrary powers of the determinant line bundle over a contact manifold. We extend the standard notions of the Heisenberg calculus: noncommutative symbolic calculus, the principal symbol, and the ...
Charles H. Conley+4 more
core +3 more sources
Introducing supersymmetric frieze patterns and linear difference operators [PDF]
We introduce a supersymmetric analog of the classical Coxeter frieze patterns. Our approach is based on the relation with linear difference operators. We define supersymmetric analogs of linear difference operators called Hill's operators.
Morier-Genoud, Sophie+2 more
core +1 more source
POINTS OF RETRACTION INTO CONE AND VORONOVSKAYA TYPE THEOREMS
The general approach to Voronovskaya theorems about the rate of convergence of linear operators sequence to the functions of some classes is considered. These theorems are proved with the help of a functional which in many concrete situations may have a ...
Yury Abakumov, Victor Banin
doaj +1 more source