Do we have anything on Banach lattices, i.e. a Banach space equipped with a lattice ordering, such that
∣x∣≤∣y∣ ⟹ ∥x∥≤∥x∥\lvert x \rvert \le \lvert y \rvert \implies \lVert x \rVert \le \lVert x \rVert∣x∣≤∣y∣⟹∥x∥≤∥x∥,
with ∣x∣=x∨−x\lvert x \rvert = x \vee -x∣x∣=x∨−x
Last updated: Dec 21 2024 at 12:33 UTC