Factorable bounded operators and Schwartz spaces

Bellenot, Steven F.

doi:10.1090/S0002-9939-1974-0328557-4

Factorable bounded operators and Schwartz spaces
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by Steven F. Bellenot PDF

Proc. Amer. Math. Soc. 42 (1974), 551-554 Request permission

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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