# On isomorphisms of some Köthe function F-spaces

Violetta Kholomenyuk; Volodymyr Mykhaylyuk; Mikhail Popov

Open Mathematics (2011)

- Volume: 9, Issue: 6, page 1267-1275
- ISSN: 2391-5455

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topVioletta Kholomenyuk, Volodymyr Mykhaylyuk, and Mikhail Popov. "On isomorphisms of some Köthe function F-spaces." Open Mathematics 9.6 (2011): 1267-1275. <http://eudml.org/doc/269237>.

@article{ViolettaKholomenyuk2011,

abstract = {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 $\mathop \{\lim \}\limits _\{\mu (A) \rightarrow 0\} \left\Vert \{\mu (A)^\{ - 1\} 1_A \} \right\Vert = 0$ (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.},

author = {Violetta Kholomenyuk, Volodymyr Mykhaylyuk, Mikhail Popov},

journal = {Open Mathematics},

keywords = {Köthe function F-spaces; Not locally convex spaces; Narrow operator; Separable quotient problem; Köthe function -spaces; non-locally convex spaces; narrow operator; separable quotient problem; Maharam set},

language = {eng},

number = {6},

pages = {1267-1275},

title = {On isomorphisms of some Köthe function F-spaces},

url = {http://eudml.org/doc/269237},

volume = {9},

year = {2011},

}

TY - JOUR

AU - Violetta Kholomenyuk

AU - Volodymyr Mykhaylyuk

AU - Mikhail Popov

TI - On isomorphisms of some Köthe function F-spaces

JO - Open Mathematics

PY - 2011

VL - 9

IS - 6

SP - 1267

EP - 1275

AB - 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 $\mathop {\lim }\limits _{\mu (A) \rightarrow 0} \left\Vert {\mu (A)^{ - 1} 1_A } \right\Vert = 0$ (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.

LA - eng

KW - Köthe function F-spaces; Not locally convex spaces; Narrow operator; Separable quotient problem; Köthe function -spaces; non-locally convex spaces; narrow operator; separable quotient problem; Maharam set

UR - http://eudml.org/doc/269237

ER -

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