In mathematics, the Bishop–Phelps theorem is a theorem about the topological properties of Banach spaces named after Errett Bishop and Robert Phelps, who published its proof in 1961.
Statement
Importantly, this theorem fails for complex Banach spaces. However, for the special case where B {\displaystyle B} is the closed unit ball then this theorem does hold for complex Banach spaces.
See also Banach–Alaoglu theorem – Theorem in functional analysis Dual norm – Measurement on a normed vector space Eberlein–Šmulian theorem – Relates three different kinds of weak compactness in a Banach space James' theorem – Theorem in mathematicsPages displaying short descriptions of redirect targets Goldstine theorem Mazur's lemma – On strongly convergent combinations of a weakly convergent sequence in a Banach space
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