论文标题
运算符空间中的非沟通规范和可凹性
Non-rough norms and dentability in spaces of operators
论文作者
论文摘要
在这项工作中，我们研究了L（X，Y）中的非循环规范，即Banach Space X和Y之间有界线性算子的空间。当且仅当X*和Y具有非俄罗斯规范时，我们证明L（x，y）具有非俄罗斯规范。我们表明，X和Y的注射量张量产物具有非冲突规范，并且仅当X和Y都有非俄罗斯规范时。我们还举例说明，在投射张量产品下，非冲突规范不稳定。我们还研究了一个相关的概念，即在L（x，y）*的背景下的小直径特性。这些结果导致讨论针对投影和注射性张量产品空间的小直径特性的稳定性。
In this work, we study non-rough norms in L(X,Y), the space of bounded linear operators between Banach spaces X and Y. We prove that L(X,Y) has non-rough norm if and only if X* and Y have non-rough norm. We show that the injective tensor product of X and Y has non-rough norm if and only if both X and Y have non-rough norm. We also give an example to show that non-rough norms are not stable under projective tensor product. We also study a related concept namely the small diameter properties in the context of L(X,Y)*. These results leads to a discussion on stability of the small diameter properties for projective and injective tensor product spaces.
