S-numbers of shift operators of formal entire functions

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 Hβp, 1 ≤ p < ∞, of formal power series f(z)=∑k=0∞akzkβ(k), equipped with the norm {norm of matrix}f{norm of matrix}=(∑k=0∞|ak|p)1p<∞, where {β (k) } is a sequence of positive numbers such that β (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.