Projections in Free Product C*-algebras Academic Article

abstract

• Consider the reduced free product of C*-algebras, (A, ) = (A1, 1) * (A2, 2), with respect to states 1 and 2 that are faithful. If 1 and 2 are traces, if the so-called Avitzour conditions are satisfied, (i.e. A1 and A2 are not "too small" in a specific sense) and if A1 and A2 are nuclear, then it is shown that the positive cone, K0(A)+, of the K0-group of A consists of those elements g K0(A) for which g = 0 or K0()(g) > 0. Thus, the ordered group K0(A) is weakly unperforated. If, on the other hand, 1 or 2 is not a trace and if a certain condition weaker than the Avitzour conditions holds, then A is properly infinite.

authors

• Dykema, Kenneth

published proceedings

• Geometric and Functional Analysis

author list (cited authors)

• Dykema, K. J., & Rrdam, M.

citation count

• 17

complete list of authors

• Dykema, KJ||Rørdam, M

publication date

• January 1998

publisher

• Springer Nature  Publisher

published in

• GEOMETRIC AND FUNCTIONAL ANALYSIS  Journal

Digital Object Identifier (DOI)

• 10.1007/s000390050046

start page

• 1

end page

• 16

volume

• 8

issue

• 1

URL

• http://dx.doi.org/10.1007/s000390050046