Spectral properties of the Rhaly operator on weighted null sequence spaces and associated operator ideals

Abstract

In this paper, a comprehensive study is made on the continuity, compactness, and spectrum of the lower triangular terraced matrix, introduced by Rhaly [[Formula: see text]-Cesaro matrices, Houston J. Math. 15(1) (1989) 137–46], 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 [Formula: see text] associated to the Rhaly operator on weighted [Formula: see text] space is defined using the concept of [Formula: see text]-number and it is proved that under certain condition, [Formula: see text] forms a quasi-Banach closed operator ideal.