Banach spaces of continuous functions on ladder system spaces

Speaker(s)

Piotr Koszmider

Affiliation

IM PAN

Language of the talk

Polish

Date

March 18, 2026, 4:15 p.m.

Room

room 4050

Seminar

Topology and Set Theory Seminar

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For every infinite cardinal kappa there are many known constructions of families of cardinality 2^kappa of pairwise nonhomeomorphic compact Hausdorff spaces of weight kappa. However, the Banach spaces C(K) and C(L) of all continuous real-valued functions  respectively on K and L with the supremum norm may be isomorphic while K and L are very far from being homeomorphic.
For every uncountable regular cardinal kappa we exhibit a family of cardinality 2^kappa of pairwise nonisomorphic Banach spaces of the form C(K) for K of weight kappa. The K's are the ladder system spaces determined by some stationary and costationary subsets of kappa.  We do not know if similar results hold in ZFC for singular kappas or even if there is in ZFC a family of cardinality 2^kappa of pairwise nonisomorphic Banach spaces of any singular density kappa and any form.
The talk is based on a part of a joint paper with M. Korpalski and W. Marciszewski available at matharxiv: https://arxiv.org/pdf/2602.09143

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