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On tame pairs of Fréchet spaces
Author(s) -
Piszczek Krzysztof
Publication year - 2009
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200610737
Subject(s) - mathematics , series (stratigraphy) , sequence (biology) , type (biology) , space (punctuation) , power series , pure mathematics , operator (biology) , sequence space , interpolation space , power (physics) , fréchet space , functional analysis , banach space , mathematical analysis , computer science , gene , repressor , ecology , chemistry , genetics , biology , operating system , paleontology , biochemistry , quantum mechanics , transcription factor , physics
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)