Abstract
The main objective of this work is to find upper bounds for s-numbers of infinite series of the forward shift operator M-z over the space H-beta(p), 1 <= p < infinity, of formal power series f(z) = Sigma(infinity)(k=0) a(k) z(k)/beta(k), equipped with the norm
parallel to f parallel to = (Sigma(infinity)(k=0)vertical bar a(k)vertical bar(p))(1/p) < infinity
where {beta(k)} is a sequence of positive numbers such that beta(0) = 1. This is done by giving exact estimations of s-numbers of powers of M-z. We apply our results to get upper estimations of s-numbers of some examples of entire functions such as the sine and exponential functions considered as a type of a right shift operator. (C) 2013 Elsevier Inc. All rights reserved.