Classical Banach Spaces II: Function Spaces

assertion assume Banach space bounded operator choice of scalars complemented subspace continuous Banach lattice converges cotype defined definition denote disjoint elements equivalent norm exists a constant fact finite follows Haar basis Hence Hölder's inequality implies inequality integer interpolation pair interpolation theorem isometric Köthe function space L₁ Lemma linear operator linear span lower q-estimate Math measurable functions measure space modulus of convexity mutually disjoint numbers o-complete order continuous Banach order isometric order isomorphic p-convexity and p-concavity positive power type probability space projection Proposition prove q-concave r.i. function space r.i. space Rademacher functions random variables remark renorming respectively result satisfies a lower satisfies an upper separable r.i. function sequence space simple function sublattice subset U₁ unconditional basis uniformly convex unit vector basis weak type weak unit X₁ X₂