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On the bidual of quasinormable Fréchet algebras

✍ Scribed by Christina P. Podara

Publisher
John Wiley and Sons
Year
2011
Tongue
English
Weight
98 KB
Volume
285
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

It is known that the bidual of a quasinormable Fréchet space E with local Banach spaces \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$(E_n)_{n\in {\mathbb N}}$\end{document} is topologically isomorphic to the inverse limit of \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\big (E_n^{\prime \prime }\big )_{n\in {\mathbb N}}$\end{document}. With the aid of the Arens product and by homological means, we prove that the previous result is equally valid for quasinormable Fréchet m‐convex algebras. This allows showing that the bidual of a σ‐C*‐algebra equipped with the Arens product is a σ‐C*‐algebra and presenting a new direct proof of a result on acyclic spectra due to Palamodov.

📜 SIMILAR VOLUMES

On tame pairs of Fréchet spaces
On tame pairs of Fréchet spaces
✍ Krzysztof Piszczek 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 206 KB

## Abstract We characterize tame pairs (__X__, __Y__) of Fréchet spaces where either __X__ or __Y__ is a power series space. For power series spaces of finite type, we get the well‐known conditions of (__DN__)‐(Ω) type. On the other hand, for power series spaces of infinite type, surprisingly, tame