数学物理学报(英文版) ›› 2018, Vol. 38 ›› Issue (4): 1163-1173.doi: 10.1016/S0252-9602(18)30806-3

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CHAIN CONDITIONS FOR C*-ALGEBRAS COMING FROM HILBERT C*-MODULES

Mahmood POURGHOLAMHOSSEIN1, Mohammad ROUZBEHANI1, Massoud AMINI2   

  1. 1. Department of Mathematics, Faculty of Sciences, University of Qom, Qom, Iran;
    2. Department of Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, 14115-134 Tehran, Iran
  • 收稿日期:2017-09-01 修回日期:2018-01-31 出版日期:2018-08-25 发布日期:2018-08-25
  • 作者简介:Mahmood POURGHOLAMHOSSEIN,E-mail:m-purghol@qom.ac.ir;Mohammad ROUZBEHANI,E-mail:mrouzbehani@stu.qom.ac.ir;Mohammad ROUZBEHANI,E-mail:mamini@modares.ac.ir

CHAIN CONDITIONS FOR C*-ALGEBRAS COMING FROM HILBERT C*-MODULES

Mahmood POURGHOLAMHOSSEIN1, Mohammad ROUZBEHANI1, Massoud AMINI2   

  1. 1. Department of Mathematics, Faculty of Sciences, University of Qom, Qom, Iran;
    2. Department of Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, 14115-134 Tehran, Iran
  • Received:2017-09-01 Revised:2018-01-31 Online:2018-08-25 Published:2018-08-25

摘要:

In this paper we define and study chain conditions for Hilbert C*-modules through their C*-algebras of compact operators and discuss their perseverance under Morita equivalence and tensor products. We show that these chain conditions are passed from the C*-algebra to its Hilbert module under certain conditions. We also study chain conditions for Hilbert modules coming from inclusion of C*-algebra with a faithful conditional expectation.

关键词: Hilbert C*-module, Noetherian and Artinian C*-algebras, purely infinite C*-algebras, Morita equivalence

Abstract:

In this paper we define and study chain conditions for Hilbert C*-modules through their C*-algebras of compact operators and discuss their perseverance under Morita equivalence and tensor products. We show that these chain conditions are passed from the C*-algebra to its Hilbert module under certain conditions. We also study chain conditions for Hilbert modules coming from inclusion of C*-algebra with a faithful conditional expectation.

Key words: Hilbert C*-module, Noetherian and Artinian C*-algebras, purely infinite C*-algebras, Morita equivalence