The Bishop-Phelps-Bollobás theorem for operators
By M. Acosta, R. Aron, Domingo García, Manuel Maestre. 2008
124 citations recorded by the source corpus.
We prove the Bishop–Phelps–Bollobas theorem for operators from an arbitrary Banach space X into a Banach space Y whenever the range space has property β of Lindenstrauss. We also characterize those Banach spaces Y for which the Bishop–Phelps–Bollobas theorem holds for operators from � 1 into Y .S everal examples of classes of such spaces are provided. For instance, the Bishop–Phelps–Bollobas theorem holds when the range space is finite-dimensional, an L1(μ)-space for a σ -finite measure μ ,a C(K)-space for a compact Hausdorff space K, or a uniformly convex Banach space.
Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/8aecdaddd9d2bdec069f78ef2ebc56c55ca01107
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In Computational Theory and Mathematics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- The Bishop-Phelps-Bollobás version of Lindenstrauss properties A and B (2013, methodology): “On the other hand, all the Yk have the AHSP since they are finite-dimensional [2].”