A basis of ${\mathbb{R}}^n$ with good isometric properties and some applications to denseness of norm attaining operators

Abstract

We characterize real Banach spaces $Y$ such that the pair $({\ell }_{\infty }^n,Y)$ has the Bishop-Phelps-Bollobás property for operators. To this purpose it is essential the use of an appropriate basis of the domain space ${\mathbb{R}}^n$. As a consequence of the mentioned characterization, we provide examples of spaces $Y$ satisfying such property. For instance, finite-dimensional spaces, uniformly convex spaces, uniform algebras and $L_1(\mu )$ ($\mu$ a positive measure) satisfy the previous property.

arXiv comment24 pages

References in corpus (5)

• The Bishop-Phelps-Bollobás version of Lindenstrauss properties A and B
• The Bishop-Phelps-Bollobás moduli of a Banach space
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Cited by in corpus (2)

• Bishop-Phelps-Bollobás property for positive operators between classical Banach spaces
• Bishop-Phelps-Bollobás property for positive operators when the domain is $L_{\infty }$