Summary: SET THEORY AND OPERATOR ALGEBRAS
ILIJAS FARAH AND ERIC WOFSEY
These notes are based on the six-hour Appalachian Set Theory workshop
given by Ilijas Farah on February 9th, 2008 at Carnegie Mellon Univer-
sity. The first half of the workshop (Sections 1-3) consisted of a review of
Hilbert space theory and an introduction to C-algebras, and the second half
(Sections 46) outlined a few set-theoretic problems relating to C-algebras.
The number and variety of topics covered in the workshop was unfortunately
limited by the available time.
Good general references on Hilbert spaces and C-algebras include ,
, , , and . An introduction to spectral theory is given in .
Most of the omitted proofs can be found in most of these references. For a
survey of applications of set theory to operator algebras, see .
Acknowledgments. We would like to thank Nik Weaver for giving us a
kind permission to include some of his unpublished results. I.F. would like to
thank George Elliott, N. Christopher Phillips, Efren Ruiz, Juris Stepr¯ans,
Nik Weaver and the second author for many conversations related to the
topics presented here. I.F. is partially supported by NSERC.
1. Hilbert spaces and operators 2