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Barrelledness of generalized sums of normed spaces

Ariel FernándezMiguel FlorencioJ. Oliveros — 2000

Czechoslovak Mathematical Journal

Let ( E i ) i I be a family of normed spaces and λ a space of scalar generalized sequences. The λ -sum of the family ( E i ) i I of spaces is λ { ( E i ) i I } : = { ( x i ) i I , x i E i , and ( x i ) i I λ } . Starting from the topology on λ and the norm topology on each E i , a natural topology on λ { ( E i ) i I } can be defined. We give conditions for λ { ( E i ) i I } to be quasi-barrelled, barrelled or locally complete.

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