标题： 数值半径极小投影 显示英文标题

标题： Minimal Projections with respect to Numerical Radius

摘要： 本文综述了关于数值半径最小化投影的一些结果。我们注意到，在情形下 $L^p$, $p=1,2,\infty$ 中，按照算子范数或者数值半径来衡量投影的最小性没有区别。然而，我们给出了从 $l^p_3$ 到二维子空间的一个投影的例子，它按范数来说是最小的，但对于 $p\neq 1,2,\infty$ 来说并不是按数值半径最小的。此外，利用Rudin的一个定理，并受傅里叶投影的启发，我们给出了按数值半径度量的最小投影的判据。另外，还给出了一些关于数值半径最小投影强唯一性的结果。 显示英文摘要

摘要： In this paper we survey some results on minimality of projections with respect to numerical radius. We note that in the cases $L^p$, $p=1,2,\infty$, there is no difference between the minimality of projections measured either with respect to operator norm or with respect to numerical radius. However, we give an example of a projection from $l^p_3$ onto a two-dimensional subspace which is minimal with respect to norm, but not with respect to numerical radius for $p\neq 1,2,\infty$. Furthermore, utilizing a theorem of Rudin and motivated by Fourier projections, we give a criterion for minimal projections, measured in numerical radius. Additionally, some results concerning strong unicity of minimal projections with respect to numerical radius are given.