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Title: Barrelledness of generalized sums of normed spaces (English)
Author: Fernández, A.
Author: Florencio, M.
Author: Oliveros, J.
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 50
Issue: 3
Year: 2000
Pages: 459-465
Summary lang: English
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Category: math
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Summary: Let $(E_{i})_{i\in I}$ be a family of normed spaces and $\lambda $ a space of scalar generalized sequences. The $\lambda $-sum of the family $(E_{i})_{i\in I}$ of spaces is \[ \lambda \lbrace (E_{i})_{i\in I}\rbrace :=\lbrace (x_{i})_{i\in I},x_{i}\in E_{i}, \quad \text{and}\quad (\Vert x_{i}\Vert )_{i\in I}\in \lambda \rbrace . \] Starting from the topology on $\lambda $ and the norm topology on each $E_i,$ a natural topology on $\lambda \lbrace (E_i)_{i\in I}\rbrace $ can be defined. We give conditions for $\lambda \lbrace (E_i)_{i\in I}\rbrace $ to be quasi-barrelled, barrelled or locally complete. (English)
Keyword: barrelled spaces
Keyword: generalized sequences
MSC: 46A08
MSC: 46A45
MSC: 46E10
MSC: 46E40
idZBL: Zbl 1079.46500
idMR: MR1777469
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Date available: 2009-09-24T10:34:42Z
Last updated: 2016-04-07
Stable URL: http://hdl.handle.net/10338.dmlcz/127585
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