On the spectrum of the lacunary Cesaro operator
DOI:
https://doi.org/10.56947/amcs.v26.444Keywords:
Lacunary sequence, Cesaro operator, Spectrum, lacunary Cesaro OperatorAbstract
In this paper, we extend the classical Cesaro operator by introducing the concept of the lacunary Cesaro operator, which incorporates the idea of lacunary sequences. We examine the operator's matrix representation and its adjoint, establishing the boundedness of these operators on Banach spaces, including the spaces of sequences that converge to zero, absolutely summable sequences, and bounded sequences. Additionally, we determine the spectrum of the operator, showing that it adapts to the structure of the underlying lacunary sequence. Notably, the spectral radius remains equal to one for a wide range of lacunary sequences.
Downloads
Downloads
Published
Issue
Section
License
Copyright (c) 2024 Annals of Mathematics and Computer Science

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.