A representation of noncommutative BMO spaces

Ali Talebi, M.S. Moslehian and Ghadir Sadeghi

Statistics & Probability Letters, 2019, vol. 153, issue C, 65-70

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).

Keywords: Noncommutative probability space; BMO space; Noncommutative Hardy space; Martingale (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1016/j.spl.2019.05.003

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