In this article we introduce the vector valued sequence space m(E k , φ, Λ), associated with the multiplier sequence Λ = (λ k ) of non-zero complex numbers, and the terms of the sequence are chosen from the semino...In this article we introduce the vector valued sequence space m(E k , φ, Λ), associated with the multiplier sequence Λ = (λ k ) of non-zero complex numbers, and the terms of the sequence are chosen from the seminormed spaces E k , seminormed by f k for all k ∈ N. This generalizes the sequence space m(φ) introduced and studied by Sargent[10]. We study some of its properties like solidity, completeness, and obtain some inclusion results. We also characterize the multiplier problem and obtain the corresponding spaces dual to m(E k , φ, Λ). We prove some general results too.展开更多
文摘In this article we introduce the vector valued sequence space m(E k , φ, Λ), associated with the multiplier sequence Λ = (λ k ) of non-zero complex numbers, and the terms of the sequence are chosen from the seminormed spaces E k , seminormed by f k for all k ∈ N. This generalizes the sequence space m(φ) introduced and studied by Sargent[10]. We study some of its properties like solidity, completeness, and obtain some inclusion results. We also characterize the multiplier problem and obtain the corresponding spaces dual to m(E k , φ, Λ). We prove some general results too.
