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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Unconditional convergence and weakly compact maps


Author: Santiago Díaz
Journal: Proc. Amer. Math. Soc. 117 (1993), 417-422
MSC: Primary 46B10; Secondary 46A08, 46B25
DOI: https://doi.org/10.1090/S0002-9939-1993-1111216-X
MathSciNet review: 1111216
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Abstract: We characterize the barrelled spaces $ E$ such that every linear continuous map from $ E$ to $ {l_1}$ carries bounded sets into relatively compact sets. These characterizations involve unconditional convergence of series, Edgar's ordering for Banach spaces, perfect sequence spaces, copies of $ {c_0}$, and Orlicz-Pettis topologies.


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DOI: https://doi.org/10.1090/S0002-9939-1993-1111216-X
Article copyright: © Copyright 1993 American Mathematical Society