Department of

Mathematics


Seminar Calendar
for events the day of Friday, March 8, 2019.

     .
events for the
events containing  

(Requires a password.)
More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
    February 2019            March 2019             April 2019     
 Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
                 1  2                   1  2       1  2  3  4  5  6
  3  4  5  6  7  8  9    3  4  5  6  7  8  9    7  8  9 10 11 12 13
 10 11 12 13 14 15 16   10 11 12 13 14 15 16   14 15 16 17 18 19 20
 17 18 19 20 21 22 23   17 18 19 20 21 22 23   21 22 23 24 25 26 27
 24 25 26 27 28         24 25 26 27 28 29 30   28 29 30            
                        31                                         

Friday, March 8, 2019

3:00 pm in 341 Altgeld Hall,Friday, March 8, 2019

Completely bounded analogues of the Choquet and Shilov boundaries for operator spaces

Raphael Clouatre (University of Manitoba)

Abstract: Given a unital operator algebra, it is natural to seek the smallest $C^*$-algebra generated by a completely isometric image of it, by analogy with the classical Shilov boundary of a uniform algebra. In keeping with this analogy, one method for constructing the so-called $C^*$-envelope is through a non-commutative version of the Choquet boundary. It is known that such a procedure can be also be applied to operator spaces, although in this case the envelope has less structure. In this talk, I will present a certain completely bounded version of the non-commutative Choquet boundary of an operator space that yields the structure of a $C^*$-algebra for the associated Shilov boundary. I will explain how the resulting $C^*$-algebras enjoy some of the properties expected of an envelope, but I will also highlight their shortcomings along with some outstanding questions about them. This is joint work with Christopher Ramsey.