Unbounded functions and positive linear operators

Positive Perturbations of Unbounded Operators

This work studies the spectral properties of certain unbounded selfadjoint operators by considering positive perturbations of such operators and the unitary equivalence of the perturbed and unperturbed transformations. Conditions are obtained on the unitary operators implementing this equivalence which guarantee that the selfadjoint operators have an absolutely continuous part.

Random Sets and Spectra of Unbounded Linear Random Operators

On some fuzzy positive and linear operators

The purpose of this work is to show that fuzzy Bernstein-Stancu operators introduced in [3] satisfy an A-statistical version of fuzzy Korovkin theorem. Some properties of these operators are also proved. An example of new fuzzy positive and linear operators is presented.

Iterative solution of linear equations with unbounded operators

A convergent iterative process is constructed for solving any solvable linear equation in a Hilbert space, including equations with unbounded, closed, densely defined linear operators. The method is proved to be stable towards small perturbation of the data. Some abstract results are established and used in an analysis of variational regularization method for equations with unbounded linear ope...

Fitzpatrick Functions and Continuous Linear Monotone Operators

The notion of a maximal monotone operator is crucial in optimization as it captures both the subdifferential operator of a convex, lower semicontinuous, and proper function and any (not necessarily symmetric) continuous linear positive operator. It was recently discovered that most fundamental results on maximal monotone operators allow simpler proofs utilizing Fitzpatrick functions. In this pa...