| Title:
|
On the “zero-two” law for positive contractions in the Banach-Kantorovich lattice $L^p(\nabla,\mu)$ (English) |
| Author:
|
Ganiev, Inomjon |
| Author:
|
Mukhamedov, Farrukh |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
47 |
| Issue:
|
3 |
| Year:
|
2006 |
| Pages:
|
427-436 |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the present paper we prove the ``zero-two'' law for positive contractions in the Banach-Kantorovich lattices $L^p(\nabla,\mu)$, constructed by a measure $\mu $ with values in the ring of all measurable functions. (English) |
| Keyword:
|
Banach-Kantorovich lattice |
| Keyword:
|
``zero-two'' law |
| Keyword:
|
positive contraction |
| MSC:
|
37A30 |
| MSC:
|
46B42 |
| MSC:
|
46E30 |
| MSC:
|
46G10 |
| MSC:
|
47A35 |
| idZBL:
|
Zbl 1150.37302 |
| idMR:
|
MR2281004 |
| . |
| Date available:
|
2009-05-05T16:58:19Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119603 |
| . |
| Reference:
|
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| Reference:
|
[CG] Chilin V.I., Ganiev I.G.: An individual ergodic theorem for contractions in the Banach-Kantorovich lattice $L^p(\nabla,\mu)$.Russian Math. (Iz. VUZ) 44 (2000), 7 77-79. MR 1803997 |
| Reference:
|
[Ga1] Ganiev I.G.: Measurable bundles of Banach lattices.Uzbek. Mat. Zh. 5 (1998), 14-21 (Russian). MR 1802533 |
| Reference:
|
[Ga2] Ganiev I.G.: Measurable bundles of metrizable topological spaces.Doklady Akad. Nauk Rep. Uzb. 4 (1999), 8-11 (Russian). |
| Reference:
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[Ga3] Ganiev I.G.: Martingales in the Banach-Kantorovich's lattices $L_p(\hat{\nabla},\hat{\mu})$.Proc. Int. Conf. Math. and its Appl. in New Millenium, Univ. Putra, Malaysia, 2001, pp,52-59. |
| Reference:
|
[GaC] Ganiev I.G., Chilin V.I.: Measurable bundles of noncommutative $L^p$-spaces associated with a center-valued trace.Siberian Adv. Math. 12 (2002), 4 19-33. MR 1984635 |
| Reference:
|
[G1] Gutman A.E.: Banach bundles in the theory of lattice-normed spaces, III.Siberian Adv. Math. 3 (1993), 4 8-40. MR 1323890 |
| Reference:
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[G2] Gutman A.E.: Banach fiberings 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). MR 1774033 |
| Reference:
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[F] Foguel S.R.: On the ``zero-two'' law.Israel J. Math. 10 (1971), 275-280. Zbl 0229.60056, MR 0298759 |
| Reference:
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[KVP] Kantorovich L.V., Vulih B.Z., Pinsker A.G.: Functional Analysis in Partially Ordered Spaces.Gosudarstv. Izdat. Tehn.-Teor. Lit., Moscow-Leningrad, 1950 (Russian). MR 0038006 |
| Reference:
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[KT] Katznelson Y., Tzafriri L.: On power bounded operators.J. Funct. Anal. 68 (1986), 313-328. Zbl 0611.47005, MR 0859138 |
| Reference:
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| Reference:
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[K2] Kusraev A.G.: Dominanted Ooperators.Mathematics and its Applications, 519, Kluwer Academic Publishers, Dordrecht, 2000. MR 1793005 |
| Reference:
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| Reference:
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[S] Sarymsakov T.A.: Topological Semifields and its Applications.Tashkent, Fan, 1989 (Russian). MR 1200017 |
| Reference:
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[V] Vulih B.Z.: Introduction to Theory of Partially Ordered Spaces.Moscow, 1961 (Russian); English translation: Wolters-Noordhoff, Groningen, 1967. MR 0224522 |
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| Reference:
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[Z1] Zaharopol R.: The modulus of a regular linear operators and the ``zero-two'' law in $L^p$-spaces $(1<p<\infty $, $p\neq 2)$.J. Funct. Anal. 68 (1986), 300-312. MR 0859137 |
| Reference:
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[Z2] Zaharopol R.: On the ``zero-two'' law for positive contractions.Proc. Edinburgh Math. Soc. 32 (1989), 363-370. Zbl 0663.47028, MR 1015480 |
| . |
