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Session 36. Topology in Functional Analysis
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Bounded convergence theorems |
Piotr Niemiec, Jagiellonian University, Poland
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The lecture will be devoted to certain results on extending continuous linear operators defined
on spaces of \(E\)-valued continuous functions (defined on a compact Hausdorff space \(X\)) to linear
operators defined on spaces of \(E\)-valued measurable functions. As an application, a new description
of uniform closures of convex subsets of \(C(X,E)\) shall be given. Also new and strong results
on integral representations of continuous linear operators defined on \(C(X,E)\) will be discussed and
new classes of vector measures and various bounded convergence theorems will be introduced.
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