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A spectral theory of linear operators on rigged Hilbert spaces under certain analyticity conditions
generalized eigenvalue resonance pole rigged Hilbert space Gelfand triplet generalized function
2011/9/22
Abstract: A spectral theory of linear operators on rigged Hilbert spaces (Gelfand triplets) is developed under the assumptions that a linear operator $T$ on a Hilbert space $\mathcal{H}$ is a perturba...
Korovkin type theorem and iterates of certain positive linear operators
Iterates of operators degree of approximation K-functionals modulus of smoothness
2011/1/18
In this paper we prove Korovkin type theorem for iterates of general positive linear operators T :C [0, 1] ! C [0, 1] and derive quantitative estimates in terms of modulus of smoothness. In particular...
Symmetric Invariant Subspaces of Complexifications of Linear Operators
Symmetric Invariant Subspaces Complexifications of Linear Operators
2011/2/22
Let T : X → X be a linear operator on a complex Banach space. Denote by (T ) and R(, T ) its spectrum and resolvent.
Korovkin-type Theorems and Approximation by Positive Linear Operators
Korovkin-type theorem positive operator approximation by positive operators
2010/12/6
This survey paper contains a detailed self-contained introduction to Korovkin-type theorems
and to some of their applications concerning the approximation of continuous functions as well
as of Lp-fu...
S-linear operators in quantum mechanics and in economy
linear operator ]tempered distribution basis linear superposition linear independence system of coordinates
2009/1/9
In this paper we study the concept of S-linear operator and we show some of
its properties and applications to the foundations of Quantum Mechanics. This
new operators are a generalization of the li...
LINEAR OPERATORS ON SOME NON-ARCHIMEDEAN HILBERT SPACES
Non-archimedean Hilbert space fractional non-archimedean Hilbert space bounded linear operator ]unbounded linear operator adjoint bounding family adj-family
2008/11/26
In this paper, we establish conditions under which a given well-defined linear operator
that is not bounded on a given non-archimedean Hilbert space would be well-defined
and bounded on another non-...
Bounded Linear Operators in Probabilistic Normed Space
Probabilistic Normed Space Bounded Linear Operators
2008/7/1
The notion of a probabilistic metric space was introduced by Menger in 1942. The notion of a probabilistic normed space was introduced in 1993. The aim of this paper is to give a necessary condition t...
Approximation by certain linear operators preserving x2
Positive linear operator polynomial weighted space degree of approximation
2010/2/25
We investigate certain positive linear operators Ln preserving the functions ek (x)=xk, k=0, 1, and modified operators Ln* which preserve e0 and e2. We show that the error of approximation of f by Ln*...
A Lower Bound for the Differences of Powers of Linear Operators
Esterle--Berkani's conjecture Quasi-nilpotent linear operator Differences of powers Decay
2007/12/11
Let $T$ be a bounded linear operator in a Banach space, with $\sigma(T) = \{1\}$. In 1983, Esterle--Berkani' s conjecture was proposed for the decay of differences $\left ( I - T \right ) T\sp{n}$ as ...
Korovkin Type Error Estimates for Positive Linear Operators Involving Some Special Functions
Positive linear operators Korovkin-Bohman theorem Bernstein power series generating function, Pochhammer symbol hypergeometric function Peetre´ s K-functional first and second order modulus of continuities functional differential equation
2010/2/25
In the present paper, we introduce a new sequence of linear positive operators with the help of generating functions. We obtain some Korovkin type approximation properties for these operators and comp...
Higher Order Generalization of Positive Linear Operators Defined by a Class of Borel Measures
Statistical convergence A-statistical convergence positive linear operators regular matrices the elements of the Lipschitz class Korovkin-type approximation theorem
2010/2/26
In the present paper, we introduce a sequence of linear operators, which is a higher order generalization of positive linear operators defined by a class of Borel measures studied in [2]. Then, using ...