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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) vol.33 no.2 Antofagasta jun. 2014

http://dx.doi.org/10.4067/S0716-09172014000200006 

 

Strongly Bounded Partial Sums

 

Charles Swartz

New Mexico State University
U. S. A.


ABSTRACT

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.


 

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Charles Swartz

Department of Mathematics
New Mexico State University
Las Cruces, NM 88003
U. S. A.
e-mail : cswartz@nmsu.edu

 

Received : February 2014. Accepted : April 2014