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Compactness in the fine and related topologies

✍ Scribed by L'. Holá; R.A. McCoy

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
92 KB
Volume
109
Category
Article
ISSN
0166-8641

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✦ Synopsis

Let X be a Tychonoff space, Y a metrizable space and C(X, Y ) be the space of continuous functions from X to Y . For a paracompact, locally hemicompact k-space X we characterize compact subsets of C(X, Y ) topologized with the fine, graph and Krikorian topologies. Our results concerning compactness in the fine topology greatly generalized those of Spring [Topology Appl. 18 (1984) 87].

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## Abstract We give __direct proofs__ of the convex compactness property for the strong operator topology in __Lebesgue spaces__ for compact or weakly compact operators. We also show how this tool applies to spectral theory of perturbed semigroups. Some non‐weakly compact operators arising in pertu