01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date:
26.09.1959
E-mail:
, , ,
Keywords:
boolean algebras,
theory vector measure,
theory measurable bundles,
dynamical systems,
noncommutative integration,
theory lattice normed spaces.
Subject:
Decomposition of Banach–Kantorovich lattices as a measurable bundles of Banach lattices are given. A representation of Boolean algebras with $L_0(Omega)$ — valued strictly positive measure as measurable bundles of boolean algebras with real valued strictly positive measure is given. A decomposition of non–commutative $L_p(М,Ф)$ space as measurable bundles of $L_p$ spaces assosiated with numerical traces is geven (with Chilin V. I.).
Biography
Graduated from Faculty of Mathematics Tashkent State University (TashSU) in 1983 (department of functional analysis). Ph.D. thesis was defended in 1990.
Doctor of science thesis was defened in 2002. A list of my works contains more than 60 titles.
Main publications:
Ganiev I. G., Chilin V. I., “Izmerimye rassloeniya nekommutativnykh $L_p$-prostranstv, assotsiirovannykh s tsentroznachnym sledom”, Matem. trudy, 4:2 (2001), 27–41
Ganiev I. G., “O vektornykh merakh so znacheniyami v prostranstvakh Banakha–Kantorovicha”, Izvestiya VUZov. Matematika, 1999, № 4, 65–67
Ganiev I. G., Kydaybergenov K. K., “Measurable bundles of compact operators”, Methods Funct. Anal. Topology, 7:4 (2001), 1–5
V. I. Chilin, I. G. Ganiev, K. K. Kudaibergenov, “The Gel'fand-Naĭmark theorem for $C^*$-algebras over a ring of measurable functions”, Izv. Vyssh. Uchebn. Zaved. Mat., 2008, no. 2, 60–68; Russian Math. (Iz. VUZ), 52:2 (2008), 58–66
V. I. Chilin, I. G. Ganiev, K. K. Kudaibergenov, “GNS-representations of $C^*$-algebras over the ring of measurable function”, Vladikavkaz. Mat. Zh., 9:2 (2007), 33–39
I. G. Ganiev, K. K. Kudaibergenov, “The Banach–Steinhaus Uniform Boundedness Principle for Operators in Banach–Kantorovich Spaces over $L^0$”, Mat. Tr., 9:1 (2006), 21–33; Siberian Adv. Math., 16:3 (2006), 42–53
I. G. Ganiev, V. I. Chilin, “Measurable Bundles of Noncommutative $L_p$-Spaces Associated with a Center-valued Trace”, Mat. Tr., 4:2 (2001), 27–41; Siberian Adv. Math., 12:4 (2002), 19–33
V. I. Chilin, I. G. Ganiev, “An individual ergodic theorem for contractions in the Banach–Kantorovich lattice $L_p(\widehat\nabla,\widehat\mu)$”, Izv. Vyssh. Uchebn. Zaved. Mat., 2000, no. 7, 81–83; Russian Math. (Iz. VUZ), 44:7 (2000), 77–79
I. G. Ganiev, Z. Saidaliev, “The Radon–Nikodým theorem for vector measures with values in a $K$-space of measurable functions”, Uspekhi Mat. Nauk, 50:2(302) (1995), 209–210; Russian Math. Surveys, 50:2 (1995), 438–439
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