数学物理学报(英文版) ›› 2017, Vol. 37 ›› Issue (4): 1019-1032.doi: 10.1016/S0252-9602(17)30055-3

• 论文 • 上一篇    下一篇

CONDITIONAL EXPECTATIONS AND MARTINGALES IN NONCOMMUTATIVE Lp-SPACES ASSOCIATED WITH CENTER-VALUED TRACES

Inomjon GANIEV1, Farrukh MUKHAMEDOV2   

  1. 1. Department of Science in Engineering, Faculty of Engineering, International Islamic University Malaysia, P. O. Box 10, 50728 Kuala-Lumpur, Malaysia;
    2. Department of Mathematical Sciences, College of Science, United Arab Emirates University, Al Ain, 15551, Abu Dhabi, UAE
  • 收稿日期:2016-03-29 修回日期:2016-07-04 出版日期:2017-08-25 发布日期:2017-08-25
  • 作者简介:Inomjon GANIEV,E-mail:inam@iium.edu.my;Farrukh MUKHAMEDOV,E-mail:far75m@yandex.ru,farrukh m@uaeu.ac.ae
  • 基金资助:

    Supported by the MOHE Grant FRGS13-071-0312.

CONDITIONAL EXPECTATIONS AND MARTINGALES IN NONCOMMUTATIVE Lp-SPACES ASSOCIATED WITH CENTER-VALUED TRACES

Inomjon GANIEV1, Farrukh MUKHAMEDOV2   

  1. 1. Department of Science in Engineering, Faculty of Engineering, International Islamic University Malaysia, P. O. Box 10, 50728 Kuala-Lumpur, Malaysia;
    2. Department of Mathematical Sciences, College of Science, United Arab Emirates University, Al Ain, 15551, Abu Dhabi, UAE
  • Received:2016-03-29 Revised:2016-07-04 Online:2017-08-25 Published:2017-08-25
  • About author:Inomjon GANIEV,E-mail:inam@iium.edu.my;Farrukh MUKHAMEDOV,E-mail:far75m@yandex.ru,farrukh m@uaeu.ac.ae
  • Supported by:

    Supported by the MOHE Grant FRGS13-071-0312.

摘要:

In this paper we prove the existence of conditional expectations in the noncommutative Lp(M, Φ)-spaces associated with center-valued traces. Moreover, their description is also provided. As an application of the obtained results, we establish the norm convergence of weighted averages of martingales in noncommutative Lp(M, Φ)-spaces.

关键词: noncommutative Lp(M, Φ)-space, Banach-Kantorovich space, measurable, conditional expectation, measurable bundle, martingale

Abstract:

In this paper we prove the existence of conditional expectations in the noncommutative Lp(M, Φ)-spaces associated with center-valued traces. Moreover, their description is also provided. As an application of the obtained results, we establish the norm convergence of weighted averages of martingales in noncommutative Lp(M, Φ)-spaces.

Key words: noncommutative Lp(M, Φ)-space, Banach-Kantorovich space, measurable, conditional expectation, measurable bundle, martingale