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Bases and quasi-reflexivity in Fréchet spaces

✍ Scribed by Manuel Valdivia

Publisher
John Wiley and Sons
Year
2005
Tongue
English
Weight
283 KB
Volume
278
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

A Fréchet space E is quasi‐reflexive if, either dim(E″/E) < ∞, or E″[β(E″,E′)]/E is isomorphic to ω. A Fréchet space E is totally quasi‐reflexive if every separated quotient is quasi‐reflexive. In this paper we show, using Schauder bases, that E is totally quasi‐reflexive if and only if it is isomorphic to a closed subspace of a countable product of quasi‐reflexive Banach spaces. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

📜 SIMILAR VOLUMES

A Characterization of the Quasi-Normable
A Characterization of the Quasi-Normable Fréchet Spaces
✍ Reinhold Meise; Dietmar Vogt 📂 Article 📅 1985 🏛 John Wiley and Sons 🌐 English ⚖ 466 KB

## Preface. The class of quasi-normable locally convex spaces has been introduced by GROTHENDIECK [4]. Recently VALDIVIA [7] and BIERSTEDT, NEISE and SUMXERS [2], [3] independently gave a characterization of the quasirnormability of the FR~CRET-KOTHE spaces A(A) resp. P ( I , A ) in terms of the K