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Linear isomorphic spaces of Cesàro-Nörlund operator, their duals and matrix transformations

Singh Uday Pratap, Jasrotia Swati, Raj Kuldip

Journal of Applied Analysis

2023

Vol. 29, nr 2

229--238

In this article, we introduce and study sequence spaces of Cesàro-Nörlund operators of order n associated with a sequence of Orlicz functions.We obtain some topological properties and Schauder basis of these sequence spaces.Moreover, we compute the α-, β- and γ-duals and the matrix transformations of these newly formed sequence spaces. Finally, we prove that these sequence spaces are of Banach-Saks type p and have a weak fixed-point property.

On Nörlund summation and ergodic theory, with applications to power series of Hilbert contractions

Cuny C., Weber M.

Bulletin of the Polish Academy of Sciences. Mathematics

2018

Vol. 66, no. 1

69--85

We show that if a = (an)n∈N is a good weight for the dominated weighted ergodic theorem in Lp, p > 1, then the Nörlund matrix Na = {ai−j / Ai}0≤j≤i, Ai = ∑ik=0|ak|, is bounded on ℓp(N). We study the regularity (convergence in norm and almost everywhere) of operators in ergodic theory: power series of Hilbert contractions and power series ∑n∈N an Pn f of L2-contractions, and establish similar close relations to the Nörlund operator associated to the modulus coefficient sequence (|an|)n∈N.