Measure of noncompactness of subsets of Lebesgue spaces

Antonín Otáhal

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On isomorphisms of some Köthe function F-spaces

Violetta Kholomenyuk, Volodymyr Mykhaylyuk, Mikhail Popov (2011)

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We prove that if Köthe F-spaces X and Y on finite atomless measure spaces (ΩX; ΣX, µX) and (ΩY; ΣY; µY), respectively, with absolute continuous norms are isomorphic and have the property $lim_{μ (A) \to 0} ∥μ {(A)}^{- 1} 1_{A}∥ = 0$ (for µ = µX and µ = µY, respectively) then the measure spaces (ΩX; ΣX; µX) and (ΩY; ΣY; µY) are isomorphic, up to some positive multiples. This theorem extends a result of A. Plichko and M. Popov concerning isomorphic classification of L p(µ)-spaces for 0 < p < 1. We also provide a new class...