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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Local automorphisms are differential operators on some Banach spaces


Authors: John C. Wells and Charles R. DePrima
Journal: Proc. Amer. Math. Soc. 40 (1973), 453-457
MSC: Primary 47B37; Secondary 47F05
MathSciNet review: 0324470
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Abstract: If $ E$ belongs to a certain category of Banach spaces (the $ {B^\infty }$-smooth spaces) which include Hilbert spaces and if $ F$ is any normed space, it is proved that any local linear automorphism of $ {C^\infty }(E,F)$ is a differential operator. This generalizes a result of J. Peetre when $ E = {R^n}$ and $ F = R$.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0324470-6
Keywords: Partial differential operators, local linear maps, smooth Banach spaces
Article copyright: © Copyright 1973 American Mathematical Society