M. D. Acosta, M. Mastyło, M. Soleimani-Mourchehkhorti
Published 2017-08-29Version 1
We study the Bishop-Phelps-Bollob\'as property for operators between Banach spaces. Sufficient conditions are given for generalized direct sums of Banach spaces with respect to a~uniformly monotone Banach sequence lattice to have the approximate hyperplane series property. This result implies that Bishop-Phelps-Bollob\'as theorem holds for operators from $\ell_1$ into such direct sums of Banach spaces. We also show that the direct sum of two spaces with the approximate hyperplane series property has such property whenever the norm of the direct sum is absolute.
On Banach spaces with the approximate hyperplane series property
Classification of Banach Spaces --its Topological and Cardinality Properties
Skipped Blocking and other Decompositions in Banach spaces
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