On isomorphisms of some Köthe function F-spaces

• Autorzy: Violetta Kholomenyuk , Volodymyr Mykhaylyuk , Mikhail Popov
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Köthe function F-spaces; Not locally convex spaces; Narrow operator; Separable quotient problem

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2011
• Tom: 9
• Numer: 6
• Strony: 1267-1275

Daty

wydano

2011-12-01

online

2011-09-23

Twórcy

autor

Violetta Kholomenyuk

• Chernivtsi National University,

autor

Volodymyr Mykhaylyuk

• Chernivtsi National University,

autor

Mikhail Popov

• Chernivtsi National University,

Bibliografia

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• [3] Maharam D., On homogeneous measure algebras, Proc. Natl. Acad. Sci. USA, 1942, 28, 108–111 http://dx.doi.org/10.1073/pnas.28.3.108
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• [5] Popov M.M., On codimension of subspaces of L p(µ) for p < 1, Funktsional. Anal. i Prilozhen., 1984, 18(2), 94–95 (in Russian) http://dx.doi.org/10.1007/BF01077844
• [6] Popov M.M., An isomorphic classification of the spaces L p for 0 < p < 1, Teor. Funktsiĭ Funktsional. Anal. i Prilozhen., 1987, 47, 77–85 (in Russian)
• [7] Rolewicz S., Metric Linear Spaces, 2nd ed., Math. Appl. (East European Ser.), 20, PWN, Warszawa, 1985
• [8] Śliwa W., The separable quotient problem for symmetric function spaces, Bull. Polish Acad. Sci. Math., 2000, 48(1), 13–27
• [9] Śliwa W., The separable quotient problem for (LF)tv-spaces, J. Korean Math. Soc., 2009, 46(6), 1233–1242 http://dx.doi.org/10.4134/JKMS.2009.46.6.1233

Identyfikatory

DOI

10.2478/s11533-011-0079-y