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On the convex compactness property for the strong operator topology and related topics
Author(s) -
MokhtarKharroubi Mustapha
Publication year - 2004
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.497
Subject(s) - compact space , mathematics , compact operator , compact operator on hilbert space , mathematical proof , approximation property , operator (biology) , regular polygon , topology (electrical circuits) , lebesgue integration , finite rank operator , operator theory , pure mathematics , discrete mathematics , banach space , combinatorics , computer science , biochemistry , chemistry , geometry , repressor , transcription factor , extension (predicate logic) , gene , programming language
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 perturbation theory of neutron transport are shown to be Dunford–Pettis operators. Copyright © 2004 John Wiley & Sons, Ltd.