Abstract characterization of Orlicz-Kantorovich lattices associated with an L 0 -valued measure

Botir Zakirov

Commentationes Mathematicae Universitatis Carolinae (2008)

  • Volume: 49, Issue: 4, page 595-610
  • ISSN: 0010-2628

Abstract

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An abstract characterization of Orlicz-Kantorovich lattices constructed by a measure with values in the ring of measurable functions is presented.

How to cite

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Zakirov, Botir. "Abstract characterization of Orlicz-Kantorovich lattices associated with an $L_0$-valued measure." Commentationes Mathematicae Universitatis Carolinae 49.4 (2008): 595-610. <http://eudml.org/doc/250473>.

@article{Zakirov2008,
abstract = {An abstract characterization of Orlicz-Kantorovich lattices constructed by a measure with values in the ring of measurable functions is presented.},
author = {Zakirov, Botir},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Orlicz-Kantorovich lattice; vector-valued measure; Orlicz function; Orlicz-Kantorovich lattice; vector-valued measure; Orlicz function},
language = {eng},
number = {4},
pages = {595-610},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Abstract characterization of Orlicz-Kantorovich lattices associated with an $L_0$-valued measure},
url = {http://eudml.org/doc/250473},
volume = {49},
year = {2008},
}

TY - JOUR
AU - Zakirov, Botir
TI - Abstract characterization of Orlicz-Kantorovich lattices associated with an $L_0$-valued measure
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2008
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 49
IS - 4
SP - 595
EP - 610
AB - An abstract characterization of Orlicz-Kantorovich lattices constructed by a measure with values in the ring of measurable functions is presented.
LA - eng
KW - Orlicz-Kantorovich lattice; vector-valued measure; Orlicz function; Orlicz-Kantorovich lattice; vector-valued measure; Orlicz function
UR - http://eudml.org/doc/250473
ER -

References

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  2. Claas W.J., Zaanen A.C., Orlicz lattices, Comment. Math. Special Issue 1 (1978), 77-93. (1978) Zbl0384.46020MR0504154
  3. Ganiev I.G., Measurable bundles of lattices and their applications, Investigations in Functional Analysis and its Applications, Nauka, Moscow, 2006, pp.9-49 (Russian). MR2272750
  4. Gutman A.E., Banach bundles in the theory of lattice-normed spaces, Order-compatible Linear Operators, Trudy Inst. Mat. 29 (1995), Izdat. Ross. Akad. Nauk Sib. Otd. Inst. Mat., Novosibirsk, 1995, pp.63-211 (Russian). Zbl0854.46006MR1774033
  5. Kantorovich L.V., Akilov G.P., Functional Analysis, Nauka, Moscow, 1977 (Russian). Zbl0555.46001MR0511615
  6. Krein S.G., Petunin Yu.T., Semenov E.M., Interpolation of Linear Operators, Nauka, Moscow, 1978 (Russian); English translation: Translations of Mathematical Monographs, vol. 54, American Mathematical Society, Providence, 1982. MR0506343
  7. Kusraev A.G., Vector Duality and its Applications, Nauka, Novosibirsk, 1985 (Russian). Zbl0616.49010MR0836135
  8. Kusraev A.G., Dominated Operators, Mathematics and its Applications, 519, Kluwer Academic Publishers, Dordrecht, 2000. Zbl1045.47001MR1793005
  9. Lacey H.E., The Isometric Theory of Classical Banach Spaces, Springer, New York-Heidelberg, 1974. Zbl0285.46024MR0493279
  10. Sarymsakov T.A., Topological Semifields and their Applications, Fan, Tashkent, 1989 (Russian). Zbl0791.54051MR1200017
  11. Vladimirov D.A., Boolean Algebras, Nauka, Moscow, 1969 (Russian). Zbl1036.06001MR0263713
  12. Vulikh B.Z., Introduction to the Theory of Partially Ordered Spaces, Fizmatgiz, Moscow, 1961 (Russian); English translation: Wolters-Noordhoff, Groningen, 1967. Zbl0186.44601MR0224522
  13. Zakirov B.S., The Luxemburg norm in the Orlicz-Kantorovich space, Uzbek. Mat. Zh. no. 2 (2007), 32-44 (Russian). (2007) MR2568484
  14. Zakirov B.S., Orlicz-Kantorovich lattices associated with an L 0 -valued measure, Uzbek. Mat. Zh. no. 4 (2007), 18-34 (Russian). (2007) Zbl1190.46035MR2569170
  15. Zakirov B.S., Analytical representation of L 0 -valued homomorphisms in Orlicz-Kantorovich modules, Mat. Trudy 10 (2007), 2 112-141 (Russian). (2007) MR2382419

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