Previous |  Up |  Next


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:
Reference: [B] Benderskiy O.Ya.: $L^p(m)$-spaces for measures with values in a topological semifield.Doklady Akad. Nauk UzSSR, 1976, n.9, 3-4 (Russian).
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: [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: [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: [F] Foguel S.R.: On the ``zero-two'' law.Israel J. Math. 10 (1971), 275-280. Zbl 0229.60056, MR 0298759
Reference: [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: [KT] Katznelson Y., Tzafriri L.: On power bounded operators.J. Funct. Anal. 68 (1986), 313-328. Zbl 0611.47005, MR 0859138
Reference: [K1] Kusraev A.G.: Vector Duality and its Applications.Novosibirsk, Nauka, 1985 (Russian). Zbl 0616.49010, MR 0836135
Reference: [K2] Kusraev A.G.: Dominanted Ooperators.Mathematics and its Applications, 519, Kluwer Academic Publishers, Dordrecht, 2000. MR 1793005
Reference: [OS] Ornstein D., Sucheston L.: An operator theorem on $L_1$ convergence to zero with applications to Markov kernels.Ann. Math. Statis. 41 (1970), 1631-1639. Zbl 0284.60068, MR 0272057
Reference: [S] Sarymsakov T.A.: Topological Semifields and its Applications.Tashkent, Fan, 1989 (Russian). MR 1200017
Reference: [V] Vulih B.Z.: Introduction to Theory of Partially Ordered Spaces.Moscow, 1961 (Russian); English translation: Wolters-Noordhoff, Groningen, 1967. MR 0224522
Reference: [W] Woyczynski W.A.: Geometry and martingales in Banach spaces.Lecture Notes in Math., vol. 472, Springer, Berlin, 1975, pp.235-283. Zbl 0353.60044, MR 0394131
Reference: [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: [Z2] Zaharopol R.: On the ``zero-two'' law for positive contractions.Proc. Edinburgh Math. Soc. 32 (1989), 363-370. Zbl 0663.47028, MR 1015480


Files Size Format View
CommentatMathUnivCarolRetro_47-2006-3_5.pdf 234.8Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo