The spectrum of q-Cesaro matrices on c and its various spectral decomposition for 0<q<1

Abstract

One of q-analogs of the Ces´aro matrix of order one is the triangular matrix with nonzero entries cnk = qn−k/1+q+···+qn , 0 k n, where q ∈ [0,1] . In this article, we will determine the spectrum of this matrix on the space of convergent sequences c . We will also obtain the fine spectral decomposition in the sense of Goldberg and a non-discrete spectral decomposition of the obtained spectrum.