Place: Bahen Centre (Room 6283)

Date: July 7th, 2017 (13:30-15:00)

Speaker: Saeed Ghasemi, Polish Academy of Sciences

Title: Scattered C*-algebras

Abstract: By the Gelfand duality, the theory of C*-algebras can be

regarded as “non-commutative topology”. In a joint work with Piotr

Koszmider at IMPAN, we investigated the non-commutative analogues of

the scattered spaces, parallel to the classical research in

set-theoretic topology. The so called scattered C*-algebras, despite

being around in the literature, have not been subject to the tools

from set-theoretic topology. The techniques and constructions of

compact, Hausdorff scattered spaces, or equivalently (by the Stone

duality) superatomic Boolean algebras, have already led to many

fundamental results in the theory of Banach spaces of the form C(K),

or more generally Asplund spaces. In fact scattered C*-algebras were

introduced as C*-algebras which are Asplund as Banach spaces. I will

introduce the notion of the Cantor-Bendixson derivatives for these

C*-algebras, and present some of the basic properties of such

algebras. I will also show how it can be used to construct C*-algebras

with exotic properties, which are non-commutative versions of

well-known scattered spaces. In particular, the constructions of

non-commutative Psi-spaces and thin tall spaces lead to new

discoveries about the preservation of the “stability” for

non-separable C*-algebras.