TY - JOUR AU - Swartz, Charles PY - 2017/03/23 Y2 - 2024/03/29 TI - Strongly Bounded Partial Sums JF - Proyecciones (Antofagasta, On line) JA - Proyecciones (Antofagasta, On line) VL - 33 IS - 2 SE - DO - 10.4067/S0716-09172014000200006 UR - https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/1288 SP - 205-213 AB - <span style="font-size: small; text-align: justify;">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.</span> ER -