Noncommutative Geometry and Topology in Prague

Soft elements in a C*-algebra

Speaker’s name:

Eduard Vilalta

Speaker’s affiliation:

Universitat Autonoma de Barcelona

Place:

This talk will take place in the blue seminar room, back building, Žitná 25.

It will also be broadcast on Zoom:

https://cesnet.zoom.us/j/91975183920?pwd=SGdlRUhLS21HUnVFTXBKcE1vYXlrQT09

Meeting ID: 919 7518 3920

Passcode: 102707

It will also be broadcast on Zoom:

https://cesnet.zoom.us/j/91975183920?pwd=SGdlRUhLS21HUnVFTXBKcE1vYXlrQT09

Meeting ID: 919 7518 3920

Passcode: 102707

Date:

Tuesday, 7. March 2023 - 16:00 to 17:00

Abstract:

The family of elements whose Cuntz class is soft plays an important role in the study of (sufficiently noncommutative) C*-algebras.

I will begin the talk by recalling what these elements are and some of the important settings where they have appeared. Using the definition of Cu-softness as an inspiration, I will define softness for positive elements in a C*-algebra and discuss their relation with their Cu-counterpart.

Having an abundance of these positive elements (in an adequate sense) characterizes the Global Glimm Property, and this can in turn be used to show that a number of C*-algebraic invariants can be computed by only looking at the soft part of a C*-algebra.

The talk is based on joint work with H. Thiel and, if time allows, the last part will be on joint work with A. Asadi-Vasfi and H. Thiel.

I will begin the talk by recalling what these elements are and some of the important settings where they have appeared. Using the definition of Cu-softness as an inspiration, I will define softness for positive elements in a C*-algebra and discuss their relation with their Cu-counterpart.

Having an abundance of these positive elements (in an adequate sense) characterizes the Global Glimm Property, and this can in turn be used to show that a number of C*-algebraic invariants can be computed by only looking at the soft part of a C*-algebra.

The talk is based on joint work with H. Thiel and, if time allows, the last part will be on joint work with A. Asadi-Vasfi and H. Thiel.