Martingal convergence theorems on JW-algebras

The concept of almost everywhere convergence and its different variants to sequesnces in von Neumann algebra were studied by many authors. There were proved many limit and ergodic theorems with respect to almost everywhere convergence in such algebras with faithful normal state. On the other hand, i...

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Main Authors:	Mukhamedov, Farrukh, Karimov , Abdusalom
Format:	Conference or Workshop Item
Language:	English
Published:	2009
Subjects:	QA Mathematics
Online Access:	http://irep.iium.edu.my/13739/ http://irep.iium.edu.my/13739/1/mf-Tashkent1-2009.pdf

id	iium-13739
recordtype	eprints
spelling	iium-137392012-01-31T04:44:35Z http://irep.iium.edu.my/13739/ Martingal convergence theorems on JW-algebras Mukhamedov, Farrukh Karimov , Abdusalom QA Mathematics The concept of almost everywhere convergence and its different variants to sequesnces in von Neumann algebra were studied by many authors. There were proved many limit and ergodic theorems with respect to almost everywhere convergence in such algebras with faithful normal state. On the other hand, in most mathematical formulations of the foundations of quantum mechanics, the bounded observables of a physical system are identified with real linear space E, of bounded selft-adjoint operators on Hilbert space H. Those bounded obervables which correspond to the projectios L from a complete orthomodular lattice P, ohterwise knowns as the lattice of the quantum logic of thephysical system. For the self adjoint operators L and y on H their Jordanprduct is difined by x a y = (xy+ yx/2 = ((x+y)2 -x2-y2)/2. So it is resonable to assume that L is JW-algebra ie. Jordan algebra of self adjoin operators on H which is closed in the weak operator topology. The main purposes of this report is to prove martingale convergence theorems in JW algebra setting. Let A be a JW-algebra with finite normal faithful trace L. LEt A be its JW-subalgebra with the unite 1. A positive unital linear mapping M(/A1): A-A1is called the conditionalexpectation wiht respect of A1 if n(xy)=r(Mx/A1)y for all x EAx y E B Let {An} be an increasing sequence of JW-subalgebras of A with conditional expectations. 2009-09 Conference or Workshop Item NonPeerReviewed application/pdf en http://irep.iium.edu.my/13739/1/mf-Tashkent1-2009.pdf Mukhamedov, Farrukh and Karimov , Abdusalom (2009) Martingal convergence theorems on JW-algebras. In: International Conference on Control and Optimization of Dynamical Systems-CODS-2009, 28-30 September, 2009, Tashkent, Uzbekistan. (Unpublished)
repository_type	Digital Repository
institution_category	Local University
institution	International Islamic University Malaysia
building	IIUM Repository
collection	Online Access
language	English
topic	QA Mathematics
spellingShingle	QA Mathematics Mukhamedov, Farrukh Karimov , Abdusalom Martingal convergence theorems on JW-algebras
description	The concept of almost everywhere convergence and its different variants to sequesnces in von Neumann algebra were studied by many authors. There were proved many limit and ergodic theorems with respect to almost everywhere convergence in such algebras with faithful normal state. On the other hand, in most mathematical formulations of the foundations of quantum mechanics, the bounded observables of a physical system are identified with real linear space E, of bounded selft-adjoint operators on Hilbert space H. Those bounded obervables which correspond to the projectios L from a complete orthomodular lattice P, ohterwise knowns as the lattice of the quantum logic of thephysical system. For the self adjoint operators L and y on H their Jordanprduct is difined by x a y = (xy+ yx/2 = ((x+y)2 -x2-y2)/2. So it is resonable to assume that L is JW-algebra ie. Jordan algebra of self adjoin operators on H which is closed in the weak operator topology. The main purposes of this report is to prove martingale convergence theorems in JW algebra setting. Let A be a JW-algebra with finite normal faithful trace L. LEt A be its JW-subalgebra with the unite 1. A positive unital linear mapping M(/A1): A-A1is called the conditionalexpectation wiht respect of A1 if n(xy)=r(Mx/A1)y for all x EAx y E B Let {An} be an increasing sequence of JW-subalgebras of A with conditional expectations.
format	Conference or Workshop Item
author	Mukhamedov, Farrukh Karimov , Abdusalom
author_facet	Mukhamedov, Farrukh Karimov , Abdusalom
author_sort	Mukhamedov, Farrukh
title	Martingal convergence theorems on JW-algebras
title_short	Martingal convergence theorems on JW-algebras
title_full	Martingal convergence theorems on JW-algebras
title_fullStr	Martingal convergence theorems on JW-algebras
title_full_unstemmed	Martingal convergence theorems on JW-algebras
title_sort	martingal convergence theorems on jw-algebras
publishDate	2009
url	http://irep.iium.edu.my/13739/ http://irep.iium.edu.my/13739/1/mf-Tashkent1-2009.pdf
first_indexed	2023-09-18T20:22:53Z
last_indexed	2023-09-18T20:22:53Z
_version_	1777408224991903744

Martingal convergence theorems on JW-algebras

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