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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Appropriate locally convex domains for differential calculus


Authors: Richard A. Graff and Wolfgang M. Ruess
Journal: Proc. Amer. Math. Soc. 86 (1982), 331-335
MSC: Primary 58C20; Secondary 46G05, 58D15
MathSciNet review: 667300
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Abstract: We make use of Grothendieck's notion of quasinormability to produce a comprehensive class of locally convex spaces within which differential calculus may be developed along the same lines as those employed within the class of Banach spaces and which include the previously known examples of such classes. In addition, we show that there exist Fréchet spaces which do not belong to any possible such class.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0667300-0
PII: S 0002-9939(1982)0667300-0
Article copyright: © Copyright 1982 American Mathematical Society