Conditional expectation on non-commutative \(H^{(r,s)}_{p}(\mathcal {A};\ell _{\infty })\) and \(H_{p}(\mathcal {A};\ell _{1})\) spaces: semifinite case

Abstract

In this paper, we investigate the conditional expectation on the non-commutative \(H^{(r,s)}_{p}(\mathcal {A};\ell _{\infty })\) and \(H_{p}(\mathcal {A};\ell _{1})\) spaces associated with semifinite subdiagonal algebra, and prove the contractibility of the underlying conditional expectation on these spaces.

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Acknowledgements

The work was partially supported by the grant (no. AP08052004 and no. AP08051978) of the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan. We thank the anonymous referee for reading the paper carefully.

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Correspondence to D. Dauitbek.

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Communicated by Yong Jiao.

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Dauitbek, D., Tulenov, K. Conditional expectation on non-commutative \(H^{(r,s)}_{p}(\mathcal {A};\ell _{\infty })\) and \(H_{p}(\mathcal {A};\ell _{1})\) spaces: semifinite case. Ann. Funct. Anal. 11, 617–625 (2020). https://doi.org/10.1007/s43034-019-00042-z

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Keywords

  • Semifinite von Neumann algebra
  • Semifinite subdiagonal algebra
  • Non-commutative Hardy spaces
  • Conditional expectation

Mathematics Subject Classification

  • 46L51
  • 46L52