[Settfa] [Set Theory]Tuesday 24 Sep, Henrik Wirzenius

[Tomasz Kania]

Hi Henrik,

I am in Innsbruck next week, sorry that I won't be able to come.

Here is my question: let X = B(H), where H = \ell_2. Does K(X) have
non-trivial ideals? Note that X fails AP.

Best wishes,
Tomek

On Sat, 21 Sept 2024 at 09:00, <kubis at math.cas.cz> wrote:

> Tuesday, 24 September 2024 - 10:00 to 11:30
> Place: IM, konírna
>
> Speaker: Henrik Wirzenius, IM CAS
> Title: Closed ideals and subideals of the Banach algebra of compact
> operators on a Banach space
>
> Abstract
>
> I will describe recent work with Hans-Olav Tylli (Helsinki) on closed
> ideals of the Banach algebra K(X) of all compact operators on a Banach
> space X. One only encounters non-trivial closed ideals of K(X) within the
> class of Banach spaces X failing the approximation property. The results
> include a Banach space Z together with an uncountable lattice of closed
> ideals of K(Z), where all of the ideals are pairwise isomorphic as Banach
> algebras. These ideals of K(Z) are not ideals of the algebra L(Z) of all
> bounded linear operators on Z; in fact, distinct closed ideals of L(X), for
> any Banach space X, are never isomorphic as Banach algebras due to a result
> of Chernoff. I will also discuss other examples of non-trivial closed
> subideals of L(X). Here a closed linear subspace I of L(X) is a non-trivial
> closed subideal if there is a closed ideal J of L(X) such that I is an
> ideal of J, but I is not an ideal of L(X).
>
> For more information see the seminar web page at
> https://www.math.cas.cz/index.php/events/seminar/6
>
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