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On tame pairs of Fréchet spaces

✍ Scribed by Krzysztof Piszczek

Publisher
John Wiley and Sons
Year
2009
Tongue
English
Weight
206 KB
Volume
282
Category
Article
ISSN
0025-584X

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✦ Synopsis

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, tameness implies boundedness of every linear and continuous operator. Next, we prove that every tame Fréchet space is quasi‐normable. This result extends earlier result of the author valid only for Köthe sequence spaces (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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