The Birkhoff-James orthogonality and norm attainment for multilinear maps

[摘要] Very recently, motivated by the result of Bhatia and Semrl which characterizes the Birkhoff-James orthogonality of operators on a finite dimensional Hilbert space in terms of norm attaining points, the Bhatia-Semrl property was introduced. The main purpose of this article is to study the denseness of the set of multilinear maps with the Bhatia-Semrl property which is contained in the set of norm attaining ones. Contrary to the most of previous results which were shown for operators on real Banach spaces, we prove the denseness for multilinear maps on some complex Banach spaces. We also show that the denseness of operators does not hold when the domain space is c(0) for arbitrary range. Moreover, we find plenty of Banach spaces Y such that only the zero operator has the Bhatia-Semrl property in the space of operators from c(0) to Y. (C) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-10-15

[关键词] Banach space;Norm attainment;Birkhoff-James orthogonality;Bhatia-Semrl property;Multilinear map