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Bishop–Phelps theorem

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.

Its statement is as follows.

Let B ⊂ E be a bounded, closed, convex set of a real Banach space E. Then the set
is norm-dense in the dual . Note, this theorem fails for complex Banach spaces [1]

See alsoEdit


  1. ^ Lomonosov, Victor (2000). "A counterexample to the Bishop-Phelps theorem in complex spaces". Israel J. Math. 115: 25–28. doi:10.1007/bf02810578.