[Settfa] Tuesday 03/10, Saeed Ghasemi

[kubis at math.cas.cz]

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 Tuesday 3rd October, 10:00am 
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 Speaker:Saeed Ghasemi, IM CAS
 Title: Non-commutative thin-tall C*-algebra

 Abstract  
A scattered space is called thin-tall if it has Cantor-Bendixson height $\omega_1$ and countable width. Similarly one can call a general scattered C*- algebra "thin-tall", if it is of height $\omega_1$ and countable width, in the Cantor-Bendixson sense. In particular, we say a thin-tall C*-algebra is "fully Non-commutative" if it is the continuous inductive limit of length $\omega_1$, of increasing set of separable essential (Approximately Finite) ideals such that each consecutive quotient is isomorphic to the algebra of all compact operators K on an infinite dimensional separable Hilbert space.  Recall that a C*-algebra is stable if it is isomorphic to its tensor product with K. I will show that there is a nonstable fully Non-commutative thin tall C*-algebra. Interestingly enough, it is well-known that (countable) inductive limits of stable C*-algebras are again stable. Therefore our construction shows that this is no longer the case for general inductive limits of
  (separable, stable, AF-) subalgebras/ideals. The construction of such algebra uses the existence of special Luzin families.
(joint work with Piotr Koszmider)
 

 For more information see the seminar web page at 
 https://calendar.math.cas.cz/set-theory-and-analysis-actual .