Wednesday, August 16, 2006

Background for Garrett

So far all I have determined for sure concerning the Garrett exposition is that one needs more background than I have on topological vector spaces and vector-valued integration/holmorphic functions. It looks so far that the most relevant references are as follows:

Bourbaki: Integration, Chapter VI, Integration Vectorielle

________: Topological Vector Spaces, Chapter III, Spaces of Continuous Linear Maps, esp. III.8, "...Quasi-complete spaces"

Rudin: Functional Analysis, Chapter 3, "Convexity", esp. the last sections on Vector-Valued Integration and Weak-Versus Strong Holmorphicity of vector-valued functions on open domains of C.

I've read most of the last and found it to be of considerable help in interpreting Garrett's cryptic comments, but haven't looked much at the Bourbaki yet.


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