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7 March 2023: Eduard Vilalta, UA Barcelona

Eduard Vilalta. Soft elements in a C*-algebra.

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

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.


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