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Factorable bounded operators and Schwartz spaces


Author: Steven F. Bellenot
Journal: Proc. Amer. Math. Soc. 42 (1974), 551-554
MSC: Primary 46B99
DOI: https://doi.org/10.1090/S0002-9939-1974-0328557-4
MathSciNet review: 0328557
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Abstract: A necessary condition for factoring continuous linear maps with domain $ {c_0}$ or $ {l_\infty }$ through a class of spaces which include the $ {l_p }$ spaces (in fact, include the $ {\mathcal{L}_p}$ spaces) for $ 2 \leqq p < \infty $ and a weaker result for $ {l_1}$ are obtained. As an application, examples of Schwartz spaces are constructed and used to answer questions of Diestel, Morris and Saxon; in particular it is shown that there are Schwartz spaces which cannot be embedded in a product of $ {l_p}$ spaces, $ 1 < p < \infty $.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0328557-4
Keywords: Factorable maps, $ {l_p}$-spaces, Schwartz spaces, nuclear spaces, varieties of topological vector spaces
Article copyright: © Copyright 1974 American Mathematical Society

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