Complemented invariant subspaces of $H ^p,\;0 < p < 1$, and the Hahn-Banach extension property

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.

Complemented Invariant Subspaces and Interpolation Sequences

It is shown that the invariant subspace of the Bergman space Ap of the unit disc, generated by a finite union of Hardy interpolation sequences, is complemented in Ap. Let D be the open unit disc of the complex plane C, and let H = H(D) denote the usual Hardy space. For 0 < p < ∞ the Bergman space A consists of analytic functions f on D such that ‖f‖p = ∫ D |f(z)| dA(z) < ∞, where dA is area mea...

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.

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...