The Orlicz Space of Entire Sequences associated with Multiplier Sequences

Abstract

Let λ = {λ1 ,λ2 , ... }be a fixed sequence of non-zero complex numbers. ΓM is the vector space of Orlicz space of entire sequences .
Let (λ) ΓM be the subset of ΓM for which { k k } M λ x ∈ Γ . In this paper, we are concerned with some properties of (λ) ΓM . In fact, for
(λ) ΓM to be equal to ΓM and for (λ) ΓM to be included in (µ) ΓM , the necessary and sufficient conditions are obtained . It is shown
that (λ) ΓM is a complete metric space if and only if liminf 0 1 > →∞ k k k λ . Furthermore, conjugate space of (λ) ΓM is obtained .