Abstract:
The purpose of this thesis is to describe in detail the structure of arbitrary operator
systems S B(H), where H is assumed to be of finite dimension, using
Arveson's non-commutative Choquet theory, and to determine the C* -envelope of
S in certain special cases of interest. Arveson classifies these operator systems as
either reduced or non-reduced, and we look at these classifications in detail. S is
said to be reduced when its boundary ideal is {0} and non-reduced otherwise. We
will give examples of 2-dimensional and 3-dimensional operator systems; show what
Arveson's parametrization would be in such cases; and determine the C*-envelopes
and boundary ideals.
Description:
A Thesis Submitted to the Faculty of Graduate Studies and Research In Partial Fulfillment of the Requirements for the Degree of Master of Science degree in Mathematics, University of Regina. v, 65 l.
