| Autor: |
Dantas, Sheldon, Jung, Mingu, Roldán, Óscar, Rueda Zoca, Abraham |
| Zdroj: |
Mediterranean Journal of Mathematics; Feb2022, Vol. 19 Issue 1, p1-27, 27p |
| Abstrakt: |
Given two Banach spaces X and Y, we introduce and study a concept of norm-attainment in the space of nuclear operators N (X , Y) and in the projective tensor product space X ⊗ ^ π Y . We exhibit positive and negative examples where both previous norm-attainment hold. We also study the problem of whether the class of elements which attain their norms in N (X , Y) and in X ⊗ ^ π Y is dense or not. We prove that, for both concepts, the density of norm-attaining elements holds for a large class of Banach spaces X and Y which, in particular, covers all classical Banach spaces. Nevertheless, we present Banach spaces X and Y failing the approximation property in such a way that the class of elements in X ⊗ ^ π Y which attain their projective norms is not dense. We also discuss some relations and applications of our work to the classical theory of norm-attaining operators throughout the paper. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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