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The Approximation Property and Locally Convex Spaces Defined by the Ideal of Approximable Operators
Author(s) -
Nelimarkka Esa
Publication year - 1982
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.19821070127
Subject(s) - mathematics , space (punctuation) , approximation property , property (philosophy) , ideal (ethics) , dual space , bounded function , regular polygon , pure mathematics , connection (principal bundle) , discrete mathematics , combinatorics , mathematical analysis , banach space , geometry , computer science , philosophy , epistemology , operating system
The connection between the approximation property and certain classes of locally convex spaces associated with the ideal of approximable operators will be discussed. It will be shown that a Frechet Montel space has the approximation property iff it is a mixed ‐space, or equivalently, iff its strong dual is a ‐space. Similarly, a Silva space has the approximation property iff it is a mixed ‐space or equivalently iff it is a ‐space. We shall also show that a Frechet Schwartz space with the bounded approximation property is always a ‐space.