Strongly Bounded Partial Sums

If λ is a scalar sequence space, a series P Zj in a topological vector space Z is λ multiplier convergent in Z if the series P ∞J =1 tj Zj converges in Z for every t = {tj} ∈ λ-If λ satisfies appropriate conditions, a series in a locally convex space X which is λ multiplier convergent in the weak topology is λ multiplier convergent in the original topology ofthe space (the Orlicz-Pettis Theorem) but may fail to be λ multiplier convergent in the strong topology of the space. However, we show under apprpriate conditions on the multiplier space λ that the series will have strongly bounded partial sums.

Saved in:
Bibliographic Details
Main Author: Swartz,Charles
Format: Digital revista
Published: Universidad Católica del Norte, Departamento de Matemáticas 2014
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!