An Orlicz-Pettis theorem for conditionally convergent series
DOI:
https://doi.org/10.22199/S07160917.1993.0002.00006Keywords:
Teoremas, EspaciosAbstract
in this note we define the idea of signed subseries convergent series in a normed linear space, and establish a result analogous to the Orlicz-Pettis theorem;
namely, that weakly siqned subseries convergent series are norm signed subseries convergent.
References
(DII) Dvoretsky, A.; Hanani, C.: Sur les changements des signes d’une serie a termes complexes. C. R. Academie Des Sciences Paris, 225 ( 1947), 516-518.
(S) Swartz, C.: An Introduction to Functional Analysis. Marcel Dekker, 1992.
(Si) Singer, I.: Bases in Banach Spaces I. Springer- Verlag New York, 1970.
(St) Stuart, C.: Weak sequential completeness of ?-duals. Preprint.
(S) Swartz, C.: An Introduction to Functional Analysis. Marcel Dekker, 1992.
(Si) Singer, I.: Bases in Banach Spaces I. Springer- Verlag New York, 1970.
(St) Stuart, C.: Weak sequential completeness of ?-duals. Preprint.
Published
2018-04-03
How to Cite
[1]
C. E. Stuart, “An Orlicz-Pettis theorem for conditionally convergent series”, Proyecciones (Antofagasta, On line), vol. 12, no. 2, pp. 155-159, Apr. 2018.
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