6533b7dafe1ef96bd126f45e

RESEARCH PRODUCT

The Bishop–Phelps–Bollobás point property

Han Ju LeeSheldon DantasSun Kwang Kim

subject

Mathematics::Functional AnalysisApplied Mathematics010102 general mathematicsBanach spaceBilinear interpolationStability resultBilinear form01 natural sciences010101 applied mathematicsCombinatoricsOperator (computer programming)Norm (mathematics)0101 mathematicsBishop–Phelps theoremAnalysisMathematics

description

Abstract In this article, we study a version of the Bishop–Phelps–Bollobas property. We investigate a pair of Banach spaces ( X , Y ) such that every operator from X into Y is approximated by operators which attain their norm at the same point where the original operator almost attains its norm. In this case, we say that such a pair has the Bishop–Phelps–Bollobas point property (BPBpp). We characterize uniform smoothness in terms of BPBpp and we give some examples of pairs ( X , Y ) which have and fail this property. Some stability results are obtained about l 1 and l ∞ sums of Banach spaces and we also study this property for bilinear mappings.

yearjournalcountryeditionlanguage
2016-12-01Journal of Mathematical Analysis and Applications
https://doi.org/10.1016/j.jmaa.2016.07.009