Vol. 63, No. 1, 1976

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Banach spaces with a restricted Hahn-Banach extension property

Charles W. Neville

Vol. 63 (1976), No. 1, 201–212

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
Received: 14 April 1975
Published: 1 March 1976
Charles W. Neville