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In this article, a comprehensive study is made on the continuity,compactness, and spectrum of the lower triangular terraced matrix, introducedby H. C. Rhaly, Jr. [Houston J. Math. 15(1): 137-146, 1989], acting on theweighted null sequence spaces with bounded, strictly positive weights. Severalspectral subdivisions such as point spectrum, residual spectrum, and continuousspectrum are also discussed. In addition, a new class of operator ideal$\chi_{c_0(r)}^{(s)}$ associated to the Rhaly operator on weighted $c_0$ spaceis defined using the concept of $s$-number and it is proved that under certaincondition, $\chi_{c_0(r)}^{(s)}$ forms a quasi-Banach closed operator ideal.

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