01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date:
25.04.1955
E-mail:
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Keywords:
order-unit space, spin-factor, Jordan akgebra, Banach algebra, von Neimann algebra.
Subject:
Spaces of intagrable elements are construction for order unit spaces with trace. Sufficient and necessary conditions of existence of predual for order unit spaces are obtained. Order unit spaces with Banach ball property are defined and conditions for the existence of traces on such spaces are found.The order unit spaces close by properties to JBW-algebras of the type I are studied.
Biography
Graduated from Faculty of Mathematics and Mechanics of Tashkent State University in 1978 (department functional analysis). Ph.D. thesis was defended in 1984. A list of my works contains more than 30 titles.
Main publications:
Berdikulov M. A. Sledy na iordanovykh algebrakh. Izv. AN UzSSR. Seriya fiz-mat. nauk. No 3. 1986. s. 10–17.
Berdikulov M. A. Order unit space of type In with banach ball property. Algebra end Operator theory. Proc. of the coll. in Tashkent. Kluwer Acad. Publishers, 1998. r. 48–53.
Berdikulov M. A. Ob odnom primere dlya spektralnykh prostranstv s poryadkovoi edinitsei odnorodnogo tipa I4. Uzb. mat. zhurn. No 3–4, 2002, s. 15–21.
Berdikulov M. A., Uslovnye ozhidaniya na prostranstvakh s poryadkovoi edinitsei. Uzb. mat. zhurn., No 1, 2003, s. 14–19.
Berdikulov M. A. Novaya poryadkovaya struktura deistvitelnykh simmetrichnykh 2kh2 matrits. Vladikavkazskii matematicheskii zhurnal. Iyul-sentyabr, 2004, Tom 6, Vypusk 3. s. 23–32.
Ayupov Sh. A., Berdikulov M. A. Zadachi teorii veroyatnostei na prostranstvakh s poryadkovoi edinitsei. Vladikavkazskii matematicheskii zhurnal. Yanvar-mart, 2005, Tom 7, Vypusk 1, s. 25–38.
Berdikulov M. A. Ponyatie sleda na prostranstvakh s poryadkovoi edinitsei i integriruemye elementy. Matematicheskie trudy, 2005, t. 8, # 2, s. 39–48.
Berdikulov M. A. Order-unit spaces wich are Banach dual spaces. Journal of Math. Physics, Analysis, Geometry, 2006, Vol. 2, No. 2, p. 130–137.
M. A. Berdikulov, “Martingale ergodic processes in Jordan Banach algebras”, Mat. Tr., 15:2 (2012), 30–36; Siberian Adv. Math., 23:3 (2013), 175–179
2008
2.
M. A. Berdikulov, “Markov Processes on Order-Unit Spaces”, Teor. Veroyatnost. i Primenen., 53:1 (2008), 153–162; Theory Probab. Appl., 53:1 (2009), 136–144
M. A. Berdikulov, “Order-unit spaces which are Banach dual spaces”, Zh. Mat. Fiz. Anal. Geom., 2:2 (2006), 130–137
2005
4.
M. A. Berdikulov, “The Notion of a Trace on Order-Unit Spaces and the Space of Integrable Elements”, Mat. Tr., 8:2 (2005), 39–48; Siberian Adv. Math., 16:2 (2006), 34–42
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