论文标题
在Crawford的数字达到运营商
On the Crawford number attaining operators
论文作者
论文摘要
我们研究了Crawford数字在Banach空间上获得运营商的密度。主要是，我们证明，如果Banach空间具有RNP，那么在有限的线性操作员的空间中，Crawford号码达到了运算符。我们还看到，在所有有界线性操作员的空间中，达到运算符的Crawford数字可能会在不吻合的情况下密集，而当Banach空间具有1个无条件的基础时，请观察到紧凑型操作员的情况。此外，我们为某些Banach空间展示了Crawford号码的Bishop-Phelps-Bollobás类型属性，我们终于讨论了有关该主题的一些困难和可能的问题。
We study the denseness of Crawford number attaining operators on Banach spaces. Mainly, we prove that if a Banach space has the RNP, then the set of Crawford number attaining operators is dense in the space of bounded linear operators. We also see among others that the set of Crawford number attaining operators may be dense in the space of all bounded linear operators while they do not coincide, by observing the case of compact operators when the Banach space has a 1-unconditional basis. Furthermore, we show a Bishop-Phelps-Bollobás type property for the Crawford number for certain Banach spaces, and we finally discuss some difficulties and possible problems on the topic.
