scholarly journals REGULARIZATION OF SOME PERTURBED INTEGRAL OPERATORS IN THE SPACES Lp

2021 ◽  
pp. 165-172
Author(s):  
Vasile Neagu
Keyword(s):  
Integral Operators ◽  
Compact Operators ◽  
Cauchy Kernel

The article presents some generalizations and refinements of the article [1]: examples of integral (non-compact) operators with point wise singularities which are admissible perturbations of the Noetherian operators are constructed; a connection between the regularizes of the perturbed and original operators is established and the equality between the indices of the perturbed and the original operators is proved. The presented results are based on the formulas obtained in this paper for the composition of an operator with the Cauchy kernel and the operators with point wise singularities.

scholarly journals A class of strongly stable operator approximations

1987 ◽  
Vol 28 (4) ◽  
pp. 435-442 ◽  
Author(s):  
Mario Ahues
Keyword(s):  
Singular Integral ◽  
Numerical Experiments ◽  
Integral Operators ◽  
Compact Operators ◽  
Singular Integral Operators ◽  
Stable Convergence ◽  
Compact Approximations

AbstractWe show the strongly stable convergence of some non-collectively-compact approximations of compact operators. Special attention is devoted to Anselone's singularity subtraction discretization of certain singular integral operators. Numerical experiments are provided.

scholarly journals Dual functors and the Radon-Nikodym property in the category of Banach spaces

1979 ◽  
Vol 27 (4) ◽  
pp. 479-494 ◽  
Author(s):  
John Wick Pelletier
Keyword(s):  
Banach Spaces ◽  
Direct Limit ◽  
Integral Operators ◽  
Compact Operators ◽  
Property A ◽  
Weakly Compact ◽  
Nikodym Property ◽  
Weakly Compact Operators

AbstractThe notion of duality of functors is used to study and characterize spaces satisfying the Radon-Nikodym property. A theorem of equivalences concerning the Radon-Nikodym property is proved by categorical means; the classical Dunford-Pettis theorem is then deduced using an adjointness argument. The functorial properties of integral operators, compact operators, and weakly compact operators are discussed. It is shown that as an instance of Kan extension the weakly compact operators can be expressed as a certain direct limit of ordinary hom functors. Characterizations of spaces satisfying the Radon-Nikodym property are then given in terms of the agreement of dual functors of the functors mentioned above.

scholarly journals Spectrum perturbations of compact operators in a Banach space

2019 ◽  
Vol 17 (1) ◽  
pp. 1025-1034
Author(s):  
Michael Gil’
Keyword(s):  
Banach Space ◽  
Integral Operators ◽  
Compact Operators ◽  
Constant Independent ◽  
Normed Ideal ◽  
Unit Operator

Abstract For an integer p ≥ 1, let Γp be an approximative quasi-normed ideal of compact operators in a Banach space with a quasi-norm NΓp(.) and the property $$\begin{array}{} \displaystyle \sum_{k=1}^{\infty} |\lambda_k(A)|^p\le a_p N_{{\it\Gamma}_p}^p(A) \;\;(A\in {\it\Gamma}_p), \end{array}$$ where λk(A) (k = 1, 2, …) are the eigenvalues of A and ap is a constant independent of A. Let A, Ã ∈ Γp and $$\begin{array}{} \displaystyle {\it\Delta}_p(A, \tilde A):= N_{{\it\Gamma}_p}(A-\tilde A) \;\exp\;\left[a_p b_p^p \;\left(1+\frac{1}2 (N_{{\it\Gamma}_p}(A+\tilde A) + N_{{\it\Gamma}_p}(A-\tilde A))\right)^p\right], \end{array}$$ where bp is the quasi-triangle constant in Γp. It is proved the following result: let I be the unit operator, I – Ap be boundedly invertible and $$\begin{array}{} \displaystyle {\it\Delta}_p(A, \tilde A)\exp\;\left[\frac{a_pN^p_{{\it\Gamma}_p}(A) } {\psi_p(A)}\right] \lt 1, \end{array}$$ where ψp(A) = infk=1,2,… |1 – $\begin{array}{} \displaystyle \lambda_k^{p} \end{array}$(A)|. Then I – Ãp is also boundedly invertible. Applications of that result to the spectrum perturbations of absolutely p-summing and absolutely (p, 2) summing operators are also discussed. As examples we consider the Hille-Tamarkin integral operators and matrices.

scholarly journals Finitely-generated solutions of certain integral equations

1994 ◽  
Vol 37 (2) ◽  
pp. 325-345 ◽  
Author(s):  
D. Porter ◽  
D. S. G. Stirling
Keyword(s):  
Integral Equation ◽  
Finite Number ◽  
Recent Work ◽  
Integral Equations ◽  
Finite Rank ◽  
Integral Operators ◽  
Compact Operators ◽  
Particular Solutions ◽  
Singular Kernels ◽  
Special Case

Recent work has shown that the solutions of the second-kind integral equation arising from a difference kernel can be expressed in terms of two particular solutions of the equation. This paper establishes analogous results for a wider class of integral operators, which includes the special case of those arising from difference kernels, where the solution of the general case is generated by a finite number of particular cases. The generalisation is achieved by reducing the problem to one of finite rank. Certain non-compact operators, including those arising from Cauchy singular kernels, are amenable to this approach.

scholarly journals Random compact operators

Filomat ◽  
2016 ◽  
Vol 30 (3) ◽  
pp. 515-523
Author(s):  
Reza Saadati
Keyword(s):  
Integral Equations ◽  
Operator Theory ◽  
Integral Operators ◽  
Compact Operators ◽  
Random Operator ◽  
Bounded Operators ◽  
Random Integral ◽  
Definition Of

Random compact operators are useful to study random differentiation and random integral equations. In this paper, we define the random norm of R-bounded operators and study random norms of differentiation operators and integral operators. The definition of random norm of R-bounded operators led us to study the random operator theory.

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