PARANORMED SPACES OF ABSOLUTE LUCAS SUMMABLE SERIES AND MATRIX OPERATORS

The aim of this paper is to introduce the absolute series space $\left\vert \mathcal{L}^{\phi }(r,s)\right\vert (\mu )$ as the the set of all series summable by the absolute Lucas method, and to give its topological and algebraic structure such as $FK-$space, duals and Schauder basis. Also, certain matrix operators on this space are characterized.

On estimates of deviation of conjugate functions from matrix operators of their Fourier series by some expressions with r-differences of the entries

We extend the results of the authors from [Abstract and Applied Analysis, Volume 2016, Article ID 9712878] to the case conjugate Fourier series.

Perturbation results in the Fredholm theory and m-essential spectra of some matrix operators

In this paper, we will use some new properties of non-compactness measure, in order to establish a description of the M-essential spectrum for some matrix operators on Banach spaces.