The Structure of the Sequence Spaces of Maddox

Grosse-Erdmann, Karl-Goswin

Canadian journal of mathematics, Tome 44 (1992) no. 2, pp. 298-307

Résumé

The sequence of spaces of Maddox, c0(p), c(p)and l ∞(p), are investigated. Here, p — (pk) is a bounded sequence of strictly positive numbers. It is observed that C0(P) is an echelon space of order 0 and that l∞(p) is a co-echelon space of order ∞, while clearly c(p) = c0(p) ⊗ 〈 (1,1,1,...) 〉. This sheds a new light on the topological and sequence space structure of these spaces: Based on the highly developed theory of (co-) echelon spaces all known and various new structural properties are derived.

Détail

DOI : 10.4153/CJM-1992-020-2

Mots-clés : 46A45

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