Very recently, motivated by the result of Bhatia and Šemrl which characterizes the Birkhoff-James orthogonality of operators on a finite dimensional Hilbert space in terms of norm attaining points, the Bhatia-Šemrl property was introduced. The main purpose of this article is to study the denseness of the set of multilinear maps with the Bhatia-Šemrl 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-Šemrl property in the space of operators from $c_0$ to Y.

最近，受Bhatia和Šemrl结果的启发，该结果以范数到达点为特征，描述了有限维希尔伯特空间上算子的Birkhoff-James正交性，并引入了Bhatia-Šemrl属性。本文的主要目的是研究规范获取集中包含的具有Bhatia-Šemrl属性的多线性映射集的稠密性。与在实际Banach空间上显示给算子的大多数先前结果相反，我们证明了某些复杂Banach空间上的多线性映射的稠密性。我们还表明，当域空间为时，运算符的密度不成立。$C_0$对于任意范围。此外，我们发现大量的Banach空间Y使得只有零算子在B算子的算子空间中具有Bhatia-Šemrl属性。$C_0$到ÿ。