Given a sequence of scalars, the Rhaly matrix is the lower triangular matrix with constant row-segments,
Let , and denote, respectively, the space of null sequences, sequences such that , and .
In [Bull. Lond. Math. Soc. 21, No. 4, 399–406 (1989; Zbl 0695.47024)], H. C. Rhaly determined the spectrum of the Rhaly operator regarded as an operator on the Hilbert space , normed by . The purpose of the present paper is to characterize the spectrum and fine spectrum of Rhaly operators acting on and .