منابع مشابه
On the Borel Complexity of Hahn-Banach Extensions
The classical Hahn-Banach Theorem states that any linear bounded functional defined on a linear subspace of a normed space admits a norm-preserving linear bounded extension to the whole space. The constructive and computational content of this theorem has been studied by Bishop, Bridges, Metakides, Nerode, Shore, Kalantari, Downey, Ishihara and others and it is known that the theorem does not a...
متن کاملQuantitative Hahn-Banach Theorems and Isometric Extensions forWavelet and Other Banach Spaces
We introduce and study Clarkson, Dol’nikov-Pichugov, Jacobi and mutual diameter constants reflecting the geometry of a Banach space and Clarkson, Jacobi and Pichugov classes of Banach spaces and their relations with James, self-Jung, Kottman and Schäffer constants in order to establish quantitative versions of Hahn-Banach separability theorem and to characterise the isometric extendability of H...
متن کاملHahn - Banach theorems
The first point here is that convex sets can be separated by linear functionals. Second, continuous linear functionals on subspaces of a locally convex topological vectorspace have continuous extensions to the whole space. Proofs are for real vectorspaces. The complex versions are corollaries. A crucial corollary is that on locally convex topological vectorspaces continuous linear functionals s...
متن کاملGeneric Hahn–Banach results
Given f : X → R ∪ {+∞} a convex and lower semi-continuous function defined on a reflexive Banach space X, and L, a closed linear manifold of X over which f takes at least a real value, the aim of this note is to prove the following Baire category result: in the Euclidean setting, the set of affine functions dominated by f on L for which there is no dominated extension to X is always of first Ba...
متن کاملHahn-banach Theorem
We prove a version of Hahn-Banach Theorem. and 1] provide the notation and terminology for this paper. The following propositions are true: (1) For all sets x, y and for every function f such that h hx; yi i 2 f holds y 2 rng f: (2) For every set X and for all functions f, g such that X dom f and f g holds fX = gX: (3) For every non empty set A and for every set b such that A 6 = fbg there exis...
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ژورنال
عنوان ژورنال: Studia Mathematica
سال: 1987
ISSN: 0039-3223,1730-6337
DOI: 10.4064/sm-85-3-299-305