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Title: Classes of C(K) spaces with few operators
Author: Schlackow, Iryna
ISNI:       0000 0004 2683 2833
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 2008
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We investigate properties of Koszmider spaces. We show that if K and L are compact Hausdor spaces with no isolated points, K is Koszmider and C(K) is isomorphic to C(L), then K and L are homeomorphic and, in particular, L is also Koszmider. We also analyse topological properties of Koszmider spaces and show that a connected Koszmider space is strongly rigid. In addition to Koszmider spaces, we introduce the notion of weakly Koszmider spaces. Having established an alternative characterisation thereof, we show that, while it is evident that every Koszmider space is weakly Koszmider, the reverse implication does not hold. We also prove that if C(K) and C(L) are isomorphic and K is weakly Koszmider, then so is L. However, if K is Koszmider, there always exists a non-Koszmider space L such that C(K) and C(L) are isomorphic. In the second part of the thesis we present two separable Koszmider spaces the construction of which does not use any set-theoretical assumptions except for the usual (ZFC) axioms. The first space is zero-dimensional, being the Stone space of a Boolean algebra. The second construction results in a separable connected Koszmider space.
Supervisor: Haydon, Richard Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Functional analysis (mathematics) ; Banach spaces ; Koszmider spaces ; few operators