NORMAL FUNCTIONALS ON LIPSCHITZ SPACES ARE WEAK* CONTINUOUS

Characterising Weak - Operator Continuous Linear Functionals on B ( H ) constructively

Abstract. Let B(H) be the space of bounded operators on a notnecessarily-separable Hilbert space H . Working within Bishop-style constructive analysis, we prove that certain weak-operator continuous linear functionals on B(H) are finite sums of functionals of the form T 〈Tx, y〉. We also prove that the identification of weakand strong-operator continuous linear functionals on B(H) cannot be esta...

Lipschitz and uniformly continuous Reducibilities on Ultrametric polish spaces

We analyze the reducibilities induced by, respectively, uniformly continuous, Lipschitz, and nonexpansive functions on arbitrary ultrametric Polish spaces, and determine whether under suitable set-theoretical assumptions the induced degree-structures are well-behaved.

Additive functionals on spaces with non-absolutely-continuous norm

Order continuous linear functionals on non-locally convex Orlicz spaces

The space of all order continuous linear functionals on an Orlicz space L defined by an arbitrary (not necessarily convex) Orlicz function φ is described.

Spaces of Lipschitz Functions on Metric Spaces

In this paper the universal properties of spaces of Lipschitz functions, defined over metric spaces, are investigated.