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On maximal non-selfadjoint reflexive algebras associated with a double triangle lattice

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Abstract

We show that the reflexive algebra Alg(ℒ) given by a double triangle lattice ℒ in a finite factor ℳ (with ℒ″ = ℳ) is maximal non-selfadjoint in the class of all weak operator closed subalgebras with the same diagonal subalgebra Alg(ℒ)∩ Alg(ℒ)*. Our method can be used to prove similar results in finite-dimensional matrix algebras. As a consequence, we give a new proof to the main theorem by Hou and Zhang (2012)

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Authors and Affiliations

  1. School of Mathematics and Computer Engineering, Xi’an University of Arts and Science, Xi’an, 710065, China

    AiJu Dong

  2. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Dong Wang

  3. Department of Mathematics and Statistics, University of New Hampshire, Durham, NH, 03824, USA

    Dong Wang

Authors
  1. AiJu Dong
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  2. Dong Wang
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Correspondence to Dong Wang.

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Dong, A., Wang, D. On maximal non-selfadjoint reflexive algebras associated with a double triangle lattice. Sci. China Math. 58, 2373–2386 (2015). https://doi.org/10.1007/s11425-015-5031-3

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  • DOI: https://doi.org/10.1007/s11425-015-5031-3

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