On the iterates of Jackson type operator GS,N in Hilbert space

Abstract

In this paper we study the limit of the iterates of Jackson type operator. Our results continue the works of Badea [2] and Nagler et al. [9, 10]. The proofs are based on spectral theory of linear operators and are performed at first for Hilbert space and then are extended for some Banach spaces.

Mathematics Subject Classification (2010): 47A10, 41A35, 41A25.

Keywords: Bounded linear operator, limit of iterates, spectral theory, Jackson type operator