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Aug 10, 2010 at 21:09 comment added Philip Brooker Just thought I'd mention that if the OP doesn't have access to a library carrying a hardcopy, or know someone who owns one, then (s)he's unlikely to find N. Tomczak-Jaegermann's book, as it's near impossible to get hold of a copy any other way. But obviously that won't matter if (s)he can get hold of Diestel, Jarchow and Tonge's book, much of which can be viewed on Google Books: books.google.com.au/…
Aug 10, 2010 at 18:13 comment added Bill Johnson Well, yes, but differentiable usually refers to an equivalent form. One of the other nice equivalences is that every set of positive measure contains a smaller set of positive measure s.t. the restriction of the operator to the functions supported on the smaller set is a compact operator.
Aug 10, 2010 at 16:11 comment added G. Rodrigues Since you mention the Lewis-Stegall paper, I presume that what you call "differentiable operators" are the representable operators, that is, those $T:L_{1}(\Omega)\to B$ for which there is a measurable a.e.-bounded $g:\Omega\to B$ such that $Tf= \int gf$, correct?
Aug 10, 2010 at 15:49 history answered Bill Johnson CC BY-SA 2.5