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On Monotone Product of Operator Algebras

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Abstract

In this note, we give complete descriptions of the structure of the monotone product of two von Neumann algebras and two C*-algebras. We show that the monotone product of two simple von Neumann algebras and C*-algebras aren’t simple again. We also show that the monotone product of two hyperfinite von Neumann algebras is again hyperfinite and determine the type of the monotone product of two factors.

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Authors and Affiliations

  1. Department of Mathematical Science, University of Tsinghua, Beijing 100084, P. R. China

    Wen Ming* Wu

  2. Department of Mathematics, Qufu Normal University, Qufu 273165, P. R. China

    Li Guang** Wang

Authors
  1. Wen Ming* Wu
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  2. Li Guang** Wang
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Corresponding authors

Correspondence to Wen Ming* Wu or Li Guang** Wang.

Additional information

*Supported by the Youth Foundation of Sichuan Education Department (China) (2003B017)

**Supported by the National Natural Science Foundation of China (10301004)

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Wu, W.M., Wang, L.G. On Monotone Product of Operator Algebras. Acta Math Sinica 23, 491–496 (2007). https://doi.org/10.1007/s10114-005-0850-8

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  • DOI: https://doi.org/10.1007/s10114-005-0850-8

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