An extension of the Kakutani–Bohnenblust characterization of $$L^p$$-spaces to $$p\in (0,\infty )$$

Abstract

AbstractFor $$p\in [1,\infty )$$ p ∈ [ 1 , ∞ ) , S. Kakutani and H.F. Bohnenblust have given characterizations of $$L^p$$ L p as a Banach lattice. We generalize that result to $$p\in (0,\infty )$$ p ∈ ( 0 , ∞ ) . In particular, we show that a quasi-Banach lattice "Equation missing" that satisfies $$\rfloor \negthickspace \rfloor u+v\lfloor \negthickspace \lfloor ^p=\rfloor \negthickspace \rfloor u\lfloor \negthickspace \lfloor ^p +\rfloor \negthickspace \rfloor v\lfloor \negthickspace \lfloor ^p$$ ⌋ ⌋ u + v ⌊ ⌊ p = ⌋ ⌋ u ⌊ ⌊ p + ⌋ ⌋ v ⌊ ⌊ p if $$u\wedge v =0$$ u ∧ v = 0 , is isometrically Riesz isomorphic to $$L^p$$ L p .