论文标题
运算符理想和张量产品的数值索引和Daugavet属性
Numerical index and Daugavet property of operator ideals and tensor products
论文作者
论文摘要
我们表明，任何操作员理想的数值索引小于或等于域和范围的数值索引的最小值。此外，我们表明，紧凑型运算符理想的数值索引或弱紧凑型操作员的理想小于或等于域的dual dual dualical索引，并且该结果提供了有趣的示例。我们还表明，Banach空间的投影或注射张量产品的数值指数小于或等于任何因素的数值索引。最后，我们表明，如果两个Banach空间的投射张量产物具有Daugavet属性，并且其中一个因素的单位球是可以计数确定的，或者其二元组包含标准的fréchet可不同性点，则另一个因素继承了Daugavet属性。如果两个Banach空间的注射张量产物具有Daugavet属性，并且其中一个因素包含范围可不同的点，则另一个因素具有Daugavet属性。
We show that the numerical index of any operator ideal is less than or equal to the minimum of the numerical indices of the domain and the range. Further, we show that the numerical index of the ideal of compact operators or the ideal of weakly compact operators is less than or equal to the numerical index of the dual of the domain, and this result provides interesting examples. We also show that the numerical index of a projective or injective tensor product of Banach spaces is less than or equal to the numerical index of any of the factors. Finally, we show that if a projective tensor product of two Banach spaces has the Daugavet property and the unit ball of one of the factor is slicely countably determined or its dual contains a point of Fréchet differentiability of the norm, then the other factor inherits the Daugavet property. If an injective tensor product of two Banach spaces has the Daugavet property and one of the factors contains a point of Fréchet differentiability of the norm, then the other factor has the Daugavet property.
