Saeed Ghasemi: Scattered C*-algebras

Place: Bahen Centre (Room 6183)

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.

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