1. Barrelledness of generalized sums of normed spaces
- Creator:
- Fernández, Ariel, Florencio, Miguel, and Oliveros, J.
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- barrelled spaces and generalized sequences
- Language:
- English
- Description:
- 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.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public