The Bishop-Phelps-Bollobas theorem for operators from l(1) sums of Banach spaces

초록

We introduce a generalized approximate hyperplane series property for a pair (X, Y) of Banach spaces to characterize when (l(1)(X), Y) has the Bishop-Phelps-Bollobas property. In particular, we show that (X, Y) has this property if X, Y are finitedimensional, if X is a C(K) space and Y is a Hilbert space, or if X is Asplund and Y = C-0(L), where K is a compact Hausdorff space and L is a locally compact Hausdorff space. (C) 2015 Elsevier Inc. All rights reserved.

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