Quasi - mackey topology
DOI:
https://doi.org/10.4067/S0716-09172007000300003Keywords:
quasi - Mackey topology, Weakly unconditionally Cauchy, Unconditionally converging operators.Abstract
Let E1, E2 be Hausdorff locally convex spaces with E2 quasi-complete, and T : E1 → E2 a continuous linear map. Then T maps bounded sets of E1 into relatively weakly compact subsets of E2 if and only if T is continuous with quasi-Mackey topology on E1. If E1 has quasi-Mackey topology and E2 is quasi-complete, then a sequentially continuous linear map T : E1 → E2 is an unconditionally converging operator.
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