Off-campus UNL users: To download campus access dissertations, please use the following link to log into our proxy server with your NU ID and password. When you are done browsing please remember to return to this page and log out.

Non-UNL users: Please talk to your librarian about requesting this dissertation through interlibrary loan.

C*-extreme points of the generalized state space of a commutative C*-algebra

Martha Case Gregg, University of Nebraska - Lincoln

Abstract

The generalized state space of a commutative C*-algebra, denoted SH(C(X)), is the set of positive unital maps from C(X) to the algebra B(H) of bounded linear operators on a Hilbert space H. C*-convexity is one of several non-commutative analogs of convexity which have been discussed in this context. We show that a C*-extreme point of SH(C(X)) satisfies a certain spectral condition on the operators in the range of an associated measure, which is a positive operator-valued measure on X. We then show that C*-extreme maps from C( X) into K+, the C*-algebra generated by the compact and scalar operators, are multiplicative, generalizing a result of D. Farenick and P. Morenz. ^

Subject Area

Mathematics

Recommended Citation

Gregg, Martha Case, "C*-extreme points of the generalized state space of a commutative C*-algebra" (2008). ETD collection for University of Nebraska - Lincoln. AAI3297903.
http://digitalcommons.unl.edu/dissertations/AAI3297903

Share

COinS