Re: example of Banach space needed

From: Michael1 <ozbourne@xxxxxx>
Date: 21 Feb 2007 07:24:45 -0500

Can you suggest me an example of
real infinite-dimensional Banach space
with a Schauder basis which admits
C^infinity partitions of unity?

Thanks, P.

--
Maarten Bergvelt
Mathematics Department, University of Illinois
Urbana-Champaign, IL 61801
Ph: 217-333-6326 email: bergv@xxxxxxxxxxxxx

Back in 1973 Henryk Torunczyk proved, that every Hilbert space, the Banach space
L_(2n)([0,1]) (n \in N) and the Banach space c_0 consisting of all real sequences tending to zero admit a C^infinity partition of unity. Just have a look at

Torunczyk, Henryk, Smooth partitions of unity on some non-separable Banach spaces, Studia. Math. 46 (1973), 43-51.

Hope this helps
Michael

.

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