Order convexity and concavity of Lorentz spaces $Λ_{p,w}$, 0 < p < ∞

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Pointwise products of some Banach function spaces and factorization (2012, background): “em 1(iv) we obtain Λφ,1 ⊙Λψ,1 = (Λ 1/2 φ,1Λ 1/2 ψ,1) (1/2) = (Λ φ1/2ψ1/2,1) (1/2) = Λ φψ,1/2 with equivalent quasi-norms. The last space is not normable since it contains isomorphic copy of l1/2 (see [KM04], Theorem 1). If 0 <pφ,I ≤qφ,I <1, then both operators H,H∗ are bounded on L∞(φ) which c”
On Lorentz spaces Γp,w (2004, methodology): “It is well known [14, 22 ] that I1 [lAp ....”