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Noncommutative Symmetric Hardy Spaces

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Abstract

Let \({\mathcal{M}}\) be a von Neumann algebra equipped with a faithful normal normalized tracial state τ. Let \({\mathcal{A}}\) be subdiagonal subalgebra of \({\mathcal{M}}\), and E be a symmetric quasi Banach space on [0, 1]. We introduce the noncommutative Hardy space \({H_{E}(\mathcal{A})}\) and transfer the recent results of the noncommutative \({H^{p}(\mathcal{A})}\) space, to the noncommutative \({H_{E}(\mathcal{A})}\) space.

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Authors and Affiliations

  1. L. N. Gumilyov Eurasian national University, Astana, 010000, Kazakhstan

    Turdebek N. Bekjan

  2. College of Mathematics and Systems Sciences, Xinjiang University, Urumqi, 830046, China

    Turdebek N. Bekjan

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  1. Turdebek N. Bekjan
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Correspondence to Turdebek N. Bekjan.

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The author is partially supported by NSFC Grant No. 11371304.

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Bekjan, T.N. Noncommutative Symmetric Hardy Spaces. Integr. Equ. Oper. Theory 81, 191–212 (2015). https://doi.org/10.1007/s00020-014-2201-6

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  • DOI: https://doi.org/10.1007/s00020-014-2201-6

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