<div dir="ltr"><div class="gmail_default" style="font-family:verdana,sans-serif;font-size:small">Hi Henrik,</div><div class="gmail_default" style="font-family:verdana,sans-serif;font-size:small"><br></div><div class="gmail_default" style="font-family:verdana,sans-serif;font-size:small">I am in Innsbruck next week, sorry that I won't be able to come.</div><div class="gmail_default" style="font-family:verdana,sans-serif;font-size:small"><br></div><div class="gmail_default" style="font-family:verdana,sans-serif;font-size:small">Here is my question: let X = B(H), where H = \ell_2. Does K(X) have non-trivial ideals? Note that X fails AP.<br></div><div class="gmail_default" style="font-family:verdana,sans-serif;font-size:small"><br></div><div class="gmail_default" style="font-family:verdana,sans-serif;font-size:small">Best wishes,</div><div class="gmail_default" style="font-family:verdana,sans-serif;font-size:small">Tomek<br></div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Sat, 21 Sept 2024 at 09:00, <<a href="mailto:kubis@math.cas.cz">kubis@math.cas.cz</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><u></u>
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Tuesday, 24 September 2024 - 10:00 to 11:30 <br>
Place: IM, konÃrna
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Speaker: Henrik Wirzenius, IM CAS<br>
Title: Closed ideals and subideals of the Banach algebra of compact operators on a Banach space
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Abstract <br>
</p><p>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).</p>
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For more information see the seminar web page at <br>
<a href="https://www.math.cas.cz/index.php/events/seminar/6" target="_blank">https://www.math.cas.cz/index.php/events/seminar/6</a>
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