showing 5 related works from this author
THE BISHOP-PHELPS-BOLLOBAS PROPERTY FOR HERMITIAN FORMS ON HILBERT SPACES
2013
On the Bishop–Phelps–Bollobás theorem for multilinear mappings
2017
Abstract We study the Bishop–Phelps–Bollobas property and the Bishop–Phelps–Bollobas property for numerical radius. Our main aim is to extend some known results about norm or numerical radius attaining operators to multilinear and polynomial cases. We characterize the pair ( l 1 ( X ) , Y ) to have the BPBp for bilinear forms and prove that on L 1 ( μ ) the numerical radius and the norm of a multilinear mapping are the same. We also show that L 1 ( μ ) fails the BPBp-nu for multilinear mappings although L 1 ( μ ) satisfies it in the operator case for every measure μ.
The Bishop–Phelps–Bollobás point property
2016
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.
The Bishop-Phelps-Bollobás property for bilinear forms and polynomials
2014
For a $\sigma$-finite measure $\mu$ and a Banach space $Y$ we study the Bishop-Phelps-Bollobás property (BPBP) for bilinear forms on $L_1(\mu)\times Y$, that is, a (continuous) bilinear form on $L_1(\mu)\times Y$ almost attaining its norm at $(f_0,y_0)$ can be approximated by bilinear forms attaining their norms at unit vectors close to $(f_0,y_0)$. In case that $Y$ is an Asplund space we characterize the Banach spaces $Y$ satisfying this property. We also exhibit some class of bilinear forms for which the BPBP does not hold, though the set of norm attaining bilinear forms in that class is dense.