Let be an infinite matrix. For a complex sequence , let be, formally, the sequence with coefficients . For any complex numbers , and (with and not simultaneously null), let be the infinite matrix with , and () and otherwise. It is well-known that defines a bounded linear operator over and with .
The paper under review deals with spectral properties of this operator over and . In particular, the authors show that the residual spectrum and the usual spectrum of over or coincide and are equal to
so the point (discrete) spectrum and the continuous spectrum are empty (here, for a complex value , will denote the unique square root of with principal argument in ).
Some results of this paper extend other ones by H. Furkan, H. Bilgiç and K. Kayaduman [Hokkaido Math. J. 35, No. 4, 893–904 (2006; Zbl 1119.47005)] and H. Furkan and K. Kayaduman [Int. Math. Forum 1, No. 21–24, 1153–1160 (2006; Zbl 1119.47306)].