Almost disjointness preserving functionals on Banach lattices of differentiable functions (Research on preserver problems on Banach algebras and related topics)

Abstract

Let C¹[0, 1] be the space of all continuously differentiable function on [0, 1]. When define the order f ≥ g by f(0) ≥ g(0) and f′ ≥ g′ pointwise on [0, 1], and the norm is defined by ∥f∥σ = |f(0)| + ∥f′∥∞, the space C¹[0, 1] is a Banach lattice. We will give the representation of bounded ε-disjointness preserving linear functionals of C¹[0, 1].