Remarks on independent sequences and dimension in topological linear spaces

Zbigniew Lipecki

Ayuda

Remarks on independent sequences and dimension in topological linear spaces

Autores: Zbigniew Lipecki
Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 49, Fasc. 1, 1998, págs. 53-66
Idioma: inglés
Enlaces
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Resumen
- We show that for a metrizable locally convex space $X$ the following conditions are equivalent: (i) every linearly independent sequence in $X$ has an $\omega$-independent subsequence; (ii) $X$ contains no subspace isomorphic to $\varphi$; (iii)$X$ admits a continuous norm. We also show that a dual Banach space equipped with the weak$^\ast$ topology satisfies (i). Moreover, we are concerned with the algebraic dimension of closed convex subsets of $F$-spaces.
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