THE SPECTRUM AND FINE SPECTRUM OF GENERALIZED RHALY-CESARO MATRICES ON c(0) AND c

Abstract

The generalized Rhaly Cesaro matrices A a are the triangular matrix with nonzero entries a(nk) = alpha(n-k)/(n+ 1) with alpha is an element of [0,1]. In [Proc. Amer. Math. Soc. 86 (1982), 405-409], Rhaly determined boundedness, compactness of generalized Rhaly Cesaro matrices on l(2) Hilbert space and shown that its spectrum is sigma (A(alpha),l(2)) = {1 /n} boolean OR {0}. Also in [32], lower bounds for these classes were obtained under certain restrictions on l(p) by Rhoades. In this paper, boundedness, compactness, spectra, the fine spectra and subdivisions of the spectra of generaled Rhaly Cesaro operator on c(0) and c have been determined.