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On isomorphisms of some Köthe function F-spaces

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Kholomenyuk V., Mykhaylyuk V., Popov M.

Open Mathematics

2011

tom 9

nr 6

1267-1275

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 $\mathop {\lim }\limits_{\mu (A) \to 0} \left\| {\mu (A)^{ - 1} 1_A } \right\| = 0$ (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.

Ograniczanie wyników

1 Open Mathematics

1 Kholomenyuk V.

1 Mykhaylyuk V.

1 Popov M.

1 2011

Wyniki wyszukiwania

On isomorphisms of some Köthe function F-spaces