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The Bishop-Phelps-Bollob'as point property | | Sheldon Dantas
; Sun Kwang Kim
; Han Ju Lee
; | | Date: |
1 May 2016 | | Abstract: | In this article, we study a version of the Bishop-Phelps-Bollob’as property.
We investigate a pair of Banach spaces $(X, Y)$ such that every operator from
$X$ into $Y$ is approximated by operators which attains its 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-Bollob’as 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 $ell_1$ and $ell_infty$ sums of Banach spaces and we also
study this property for bilinear mappings. | | Source: | arXiv, 1605.0245 | | Services: | Forum | Review | PDF | Favorites | |
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