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Proceedings of the American Mathematical Society

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A simple example of a universal Schwartz space


Author: Daniel J. Randtke
Journal: Proc. Amer. Math. Soc. 37 (1973), 185-188
MSC: Primary 46A05; Secondary 46F05
DOI: https://doi.org/10.1090/S0002-9939-1973-0312192-7
MathSciNet review: 0312192
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Abstract: A Schwartz space E is universal if every Schwartz space is topologically isomorphic to a linear subspace of some power $ {E^I}$ of E. In this paper concrete examples of universal Schwartz spaces are exhibited.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0312192-7
Keywords: Schwartz space, universal Schwartz space, precompact seminorm, precompact operator, compact operator
Article copyright: © Copyright 1973 American Mathematical Society