Unconditional convergence and weakly compact maps

Díaz, Santiago

doi:10.1090/S0002-9939-1993-1111216-X

Unconditional convergence and weakly compact maps
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by Santiago Díaz

Proc. Amer. Math. Soc. 117 (1993), 417-422

DOI: https://doi.org/10.1090/S0002-9939-1993-1111216-X

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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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