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RESEARCH PRODUCT
On the Bishop–Phelps–Bollobás theorem for multilinear mappings
Domingo GarcíaManuel MaestreSun Kwang KimHan Ju LeeSheldon Dantassubject
Discrete mathematicsNumerical AnalysisMultilinear mapAlgebra and Number Theory010102 general mathematicsBilinear form01 natural sciences010101 applied mathematicsOperator (computer programming)Discrete Mathematics and CombinatoricsGeometry and Topology0101 mathematicsBishop–Phelps theoremMathematicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2017-11-01 | Linear Algebra and its Applications |