[Settfa] Tuesday 24/01, Saeed Ghasemi
kubis at math.cas.cz
kubis at math.cas.cz
Thu Jan 19 19:00:02 CET 2017
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Tuesday 24th January, 10:00am
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Speaker:Saeed Ghasemi, Institute of Mathematics, Polish Academy of Sciences
Title: On scattered C*-algebras
Abstract
By the Gelfand duality it is well-known that 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. Scattered C*-algebras were
introduced as C*-algebras which are Asplund as Banach spaces. I will
introduce these C*-algebras, the notion of the Cantor-Bendixson
derivatives for them, and present some of the basic properties of such
algebras. I will also show how it can be used to construct exotic
C*-algebras 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 "stability of
extensions of C*-algebras".
For more information see the seminar web page at
https://calendar.math.cas.cz/set-theory-and-analysis-actual .
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