论文标题
关于沙顿限制规范
On Schatten restricted norms
论文作者
论文摘要
我们考虑在复杂的可分开的希尔伯特空间上的规范，以便$ \ langle a了，ξ\ rangle \ leq \ | eC \ | | |^2 \ leq \ leq \ langlebξ，ξ\ rangle $对于正面可逆操作员$ a $ a $ a $和$ b $与Schatten Classe Operator不同。我们证明这些规范具有可单位化的等轴测组，我们的证明使用固定点定理的概括用于对正逆转算子的等轴测动作。结果，如果等轴测组不留下任何有限的尺寸子空间不变，则必须是希尔伯特人。也就是说，如果将希尔伯特式的规范更改为紧密的非希尔伯特式规范，那么等轴测组确实会留下有限的维度子空间不变。该方法涉及与该组对身份阳性可逆的schatten扰动的非物质弯曲空间的规范作用有关的公制几何参数。
We consider norms on a complex separable Hilbert space such that $\langle aξ,ξ\rangle\leq\|ξ\|^2\leq\langle bξ,ξ\rangle$ for positive invertible operators $a$ and $b$ that differ by an operator in the Schatten class. We prove that these norms have unitarizable isometry groups, our proof uses a generalization of a fixed point theorem for isometric actions on positive invertible operators. As a result, if the isometry group does not leave any finite dimensional subspace invariant, then the norm must be Hilbertian. That is, if a Hilbertian norm is changed to a close non-Hilbertian norm, then the isometry group does leave a finite dimensional subspace invariant. The approach involves metric geometric arguments related to the canonical action of the group on the non-positively curved space of positive invertible Schatten perturbations of the identity .
