On isomorphisms of some Köthe function F-spaces
Violetta Kholomenyuk ; Volodymyr Mykhaylyuk ; Mikhail Popov
Open Mathematics, Tome 9 (2011), p. 1267-1275 / Harvested from The Polish Digital Mathematics Library
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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 limμ(A)→0μ(A)-11A=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 of F-spaces having no nonzero separable quotient space.

Publié le : 2011-01-01
EUDML-ID : urn:eudml:doc:269237 
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     title = {On isomorphisms of some K\"othe function F-spaces},
     journal = {Open Mathematics},
     volume = {9},
     year = {2011},
     pages = {1267-1275},
     zbl = {1238.46002},
     language = {en},
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Violetta Kholomenyuk; Volodymyr Mykhaylyuk; Mikhail Popov. On isomorphisms of some Köthe function F-spaces. Open Mathematics, Tome 9 (2011) pp. 1267-1275. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0079-y/

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