Abstract:
This dissertation explores the application of quasitraces to automorphisms and antiautomorphisms, analyzes analogs of hyperfiniteness in complex and real $AW^\ast$-algebras, and examines the connection between quasitraces and concepts such as finiteness and infiniteness in $C^\ast$- and $AW^\ast$-algebras. The thesis presents an analog of the definition of hyperfiniteness for $AW^\ast$-algebras, a real analog of a quasitrace, and demonstrates its connection to the complex counterpart. It is proved that the stable finiteness of real $C^\ast $-algebras can be reduced to a similar question for $AW^\ast$-algebras. It is also established that an $AW^\ast$-algebra is finite if and only if its complexification is finite. A real analog of the concept of “proper infiniteness” is given through the definition of a real quasitrace. It is shown that a traceless real $C^\ast$-algebra is purely infinite, and if such an algebra is also an $AW^\ast$-algebra, then it is of type III.
Website:
https://us02web.zoom.us/j/8022228888?pwd=b3M4cFJxUHFnZnpuU3kyWW8vNzg0QT09
|
