The Orlicz Space of Entire Sequences associated with Multiplier Sequences

摘要

Γbe the subset of MΓ for which {}MkkxΓ∈λ . In this paper, we are concerned with some properties of ()λMΓ. In fact, for ()λMΓ to be equal to MΓand for ()λMΓ to be included in ()μMΓ, the necessary and sufficient conditions are obtained . It is shown that ()λMΓ is a complete metric space if and only if 0 inflim1>∞→kkkλ. Furthermore, conjugate space of ()λMΓ is obtained .