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A representation of noncommutative BMO spaces

Author

Listed:
  • Talebi, Ali
  • Moslehian, M.S.
  • Sadeghi, Ghadir

Abstract

It is known that the noncommutative Hardy spaces H1(M) and H1max(M) do not coincide, in general. In fact, it may happen that H1(M)⊈H1max(M). It is an interesting question whether the reverse inclusion holds or not. In this note, motivated by this question, we prove that the validity of inequality ‖x‖H1C(M)≤c‖x‖H1max(M) for some c and all martingales x∈H1max(M) gives rise to a certain representation of positive elements of the noncommutative space BMO. Conversely, existence of such a representation for elements of BMO yields the inequality above for positive martingales of H1max(M).

Suggested Citation

  • Talebi, Ali & Moslehian, M.S. & Sadeghi, Ghadir, 2019. "A representation of noncommutative BMO spaces," Statistics & Probability Letters, Elsevier, vol. 153(C), pages 65-70.
    • Handle: RePEc:eee:stapro:v:153:y:2019:i:c:p:65-70
    DOI: 10.1016/j.spl.2019.05.003
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