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Banach spaces with a
restricted Hahn-Banach extension property
Charles W. Neville |
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Vol. 63 (1976), No. 1, 201–212
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Abstract |
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We shall study the class of real Banach spaces B with the following restricted Hahn-Banach extension property: For each Banach space C with a dense set of cardinality ≦ some fixed cardinal N, and for each subspace A of C and bounded linear map T0 : A → B, there exists an extension T : C → B such that ∥T∥ = ∥T0∥. Suprisingly, there exist Banach spaces in this class which are not isometrically isomorphic to C(X) for a compact Hausdorff X! |
Mathematical Subject Classification 2000
Primary: 46B05, 46B05
Secondary: 46M10
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Milestones
Received: 14 April 1975
Published: 1 March 1976
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Authors |
| Charles W. Neville | |
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