C(K)-spaces with few operators relative to posets

Speaker(s)

Antonio Acuaviva

Affiliation

Lancaster University

Language of the talk

Polish

Date

May 13, 2026, 4:15 p.m.

Room

room 4050

Seminar

Topology and Set Theory Seminar

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Understanding the closed operator ideals of the algebra of operators on a Banach space is a natural but often difficult problem. In this talk, we will focus on the case of spaces of continuous functions, C(K).
After discussing some of the difficulties that arise in the classical separable setting, we will turn to examples of C(K)-spaces with few operators, where K is obtained through Mrówka-Isbell constructions associated with almost disjoint families. In particular, we will describe how a construction of Koszmider and Laustsen can be extended relative to a partially ordered set P, producing families of C(K)-spaces whose operator structure reflects the order structure of P. This leads to new examples for which the closed operator ideals can be completely classified.
The talk is partially based on the author's preprint C(K)-spaces with few operators relative to posets, available as arXiv:2511.22339.

 

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