摘要
Let X be a Banach space and be a sequence in X. The author shows that is a basic sequence if and only if converges for every j≥1 and holds for every choice of scalar variables {αnj} such that converges for each n≥ 1 and any choice of scalar variables {rn} such that converges. Moreover, some applications about the result are given.
Let X be a Banach space and be a sequence in X. The author shows that is a basic sequence if and only if converges for every j≥1 and holds for every choice of scalar variables {αnj} such that converges for each n≥ 1 and any choice of scalar variables {rn} such that converges. Moreover, some applications about the result are given.
基金
Natural Science and Education Foundationof Henan Province and Young Fundation of Henan Normal University
