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The Structure of the Sequence Spaces of Maddox

Published online by Cambridge University Press:  20 November 2018

Karl-Goswin Grosse-Erdmann
Karl-Goswin Grosse-Erdmann*
Affiliation:
Fachbereich Mathematik und Informatik Fern Universität Hagen—Gesamthochschule— Postfach 940 D-5800 Hagen, Germany
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Abstract

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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.

Keywords

46A45
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 44 , Issue 2 , 01 April 1992 , pp. 298 - 307
Copyright
Copyright © Canadian Mathematical Society 1992

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