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Tuesday, 25 November 2025 - 10:00 to 11:30 <br />
Place: IM, konírna
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Speaker: Zdeněk Silber, Institute of Mathematics, Czech Academy of Sciences<br />
Title: On subspaces of indecomposable Banach spaces
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Abstract <br />
<p>In the talk we adress the following question: What Banach spaces are isomorphic to subspaces of indecomposable Banach spaces? Recall that a Banach space is indecomposable if it cannot be “decomposed” as a direct sum of two infinite dimensional subspaces. A well-known class of indecomposable spaces are hereditarily indecomposable spaces, first constucted by Gowers and Maurey, but our question makes no sense for them, as clearly any subspace of a hereditarily indecomposable space is itself hereditarily indecomposable. Hence, we will rather work in the class of indecomposable C(K) spaces, introduced by Koszmider. Certainly not all spaces can be embedded in an indecomposable space – for example l_infinity cannot and neither can any injective space. We show that the class of spaces that can be embedded in an indecomposable spaces is quite large – it contains all spaces of density at most continuum which do not admit l_infinity as a quotient (this includes e.g. Asplund or WLD spaces). We also show that there is an indecomposable C(K) space that does admit l_infinity as a quotient. The general question thus remains open for Banach spaces (of density at most continuum) that do admit l_infinity as a quotient but not as a subspace. </p><p>This is a joint work with Piotr Koszmider.</p>
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For more information see the seminar web page at <br />
https://www.math.cas.cz/index.php/events/seminar/6
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Set Theory and Analysis mailing list <br />
settfa@math.cas.cz <br />
https://list.math.cas.cz/listinfo/settfa@math.cas.cz
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