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

  • D. DauitbekEmail author
  • K. Tulenov
Original Paper

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.

Keywords

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

Mathematics Subject Classification

46L51 46L52 

Notes

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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Copyright information

© Tusi Mathematical Research Group (TMRG) 2019

Authors and Affiliations

  1. 1.Abai Kazakh National Pedagogical UniversityAlmatyKazakhstan
  2. 2.Institute of Mathematics and Mathematical ModelingAlmatyKazakhstan
  3. 3.Al-Farabi Kazakh National UniversityAlmatyKazakhstan

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