Some results on noncommutative Hardy-Lorentz spaces

Abstract

Let A be a maximal subdiagonal algebra of a finite von Neumann algebra M. For 0 < p < ∞, we define the noncommutative Hardy-Lorentz spaces and establish the Riesz and Szegö factorizations on these spaces. We also present some results of Jordan morphism on these spaces. MSC: 46L53; 46L51

Noncommutative Hardy–Lorentz spaces associated with semifinite subdiagonal algebras

“…Since ω ∈ B p ∩ B * ∞ , then Corollary 2.3 and Proposition 2.6 of [1] imply that 1 < α Λ p ω ≤ β Λ p ω < ∞. From Proposition 3.1 of [11], we obtain…”

“…where ω(t) = t q W (t) −q ω(t), t > 0, [8] mean that Λ p ω (M) is an interpolation space for the couple (L 1 (M), M). Therefore, by slightly modifying the proof of Proposition 2.4 and Proposition 2.6 in [11], we can prove (1)-( 3) and omit the details.…”

“…Therefore, Theorem 3.7 of [8] means that Λ p ω (M) is an interpolation space for the couple (L r (M), M), 1 ≤ r < α Λ p ω . By Lemma 6.5(iii) of [4] and Proposition 3.7, there exist two constants C 0 , C 1 > 0 such that [11] means that…”