标题： Lipschitz 与线性数值指数在某些巴拿赫空间中 显示英文标题

标题： Lipschitz vs Linear Numerical Index in certain Banach spaces

摘要： 我们证明了对于实巴拿赫空间，如果它们是可分的或对偶空间，那么Lipschitz数值指数与经典的（线性）数值指数一致。 这一结果为Wang、Huang和Tan（2014）提出的问题提供了部分证据，即这两个量是否在每个实巴拿赫空间中都一致。 我们的方法依赖于两种标准的Lipschitz映射线性化技术：通过高斯概率测度的卷积进行微分，以及不变均值。 显示英文摘要

摘要： We show that for real Banach spaces that are either separable or dual spaces, the Lipschitz numerical index coincides with the classical (linear) numerical index. This result provides partial evidence toward the question posed by Wang, Huang, and Tan (2014) of whether these two quantities coincide for every real Banach space. Our approach relies on two standard linearization techniques for Lipschitz maps: differentiation via convolution with Gaussian probability measures, and invariant means.