Complemented subspaces and the Hahn-Banach extension property in lp(0 < p < 1)

On the Hahn-banach Extension Property

A self-contained and brief proof is given of the equivalence of the Hahn-Banach extension property (HB) and the conditional order completeness of the range space (LUB). Various other equivalences are discussed.

On quasi-complemented subspaces of banach spaces.

Hahn-Banach extension theorems for multifunctions revisited

Several generalizations of the Hahn–Banach extension theorem to K-convex multifunctions were stated recently in the literature. In this note we provide an easy direct proof for the multifunction version of the Hahn–Banach–Kantorovich theorem and show that in a quite general situation it can be obtained from existing results. Then we derive the Yang extension theorem using a similar proof as wel...

The Hahn-Banach Property and the Axiom of Choice

We work in the set theory without the axiom of choice: ZF. Though the Hahn-Banach theorem cannot be proved in ZF, we prove that every Gâteauxdifferentiable uniformly convex Banach space E satisfies the following continuous Hahn-Banach property: if p is a continuous sublinear functional on E, if F is a subspace of E, and if f : F → R is a linear functional such that f ≤ p|F , then there exists a...

A FUZZY VERSION OF HAHN-BANACH EXTENSION THEOREM

In this paper, a fuzzy version of the analytic form of Hahn-Banachextension theorem is given. As application, the Hahn-Banach theorem for$r$-fuzzy bounded linear functionals on $r$-fuzzy normedlinear spaces is obtained.