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- W2061750446 abstract "Given any subspace N of a Banach space X , there is a subspace M containing N and of the same density character as N , for which there exists a linear Hahn–Banach extension operator from M * to X *. This result was first proved by Heinrich and Mankiewicz [ 4 , Proposition 3.4] using some of the deeper results of Model Theory. More precisely, they used the Banach space version of the Löwenheim–Skolem theorem due to Stern [ 11 ], which in turn relies on the Löwenheim–Skolem and Keisler–Shelah theorems from Model Theory. Previously Lindenstrauss [ 7 ], using a finite dimensional lemma and a compactness argument, obtained a version of this for reflexive spaces. We shall show that the same finite dimensional lemma leads directly to the general result, without any appeal to Model Theory." @default.
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- W2061750446 date "1989-02-01" @default.
- W2061750446 modified "2023-09-30" @default.
- W2061750446 title "Linear Hahn–Banach extension operators" @default.
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- W2061750446 doi "https://doi.org/10.1017/s0013091500006908" @default.
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