Analysis and Probability Seminar

The multiplier algebra of a C*-algebra is the non-commutative generalization of the Stone–Čech compactification of a topological space. An interesting and often deep question about this construction is the preservation of certain properties, that is, given a C*-algebra A that satisfies a certain property P, when does its multiplier M(A) satisfy P?

In this talk, I will recall the construction of the multiplier algebra and focus on the question above for the property of nowhere scatteredness. This notion, which ensures sufficient noncommutativity of a C*-algebra, does not always pass to multiplier algebras. Surprisingly, regularity properties play a role in this study. During the talk, I will give sufficient conditions under which nowhere scatteredness is preserved. I will also give some examples of nowhere scattered C*-algebras whose multiplier algebra is not nowhere scattered.