Spectral properties of the Rhaly operator on weighted null sequence spaces and associated operator ideals
Spectral Theory
2023-05-09 v1
Abstract
In this article, a comprehensive study is made on the continuity, compactness, and spectrum of the lower triangular terraced matrix, introduced by H. C. Rhaly, Jr. [Houston J. Math. 15(1): 137-146, 1989], acting on the weighted null sequence spaces with bounded, strictly positive weights. Several spectral subdivisions such as point spectrum, residual spectrum, and continuous spectrum are also discussed. In addition, a new class of operator ideal associated to the Rhaly operator on weighted space is defined using the concept of -number and it is proved that under certain condition, forms a quasi-Banach closed operator ideal.
Keywords
Cite
@article{arxiv.2305.04624,
title = {Spectral properties of the Rhaly operator on weighted null sequence spaces and associated operator ideals},
author = {Arnab Patra and Jyoti Rani and Sanjay Kumar Mahto},
journal= {arXiv preprint arXiv:2305.04624},
year = {2023}
}