关于规范一多项式的多项式数值指数

On the numerical index of absolute symmetric norms on the plane

We give a lower bound for the numerical index of two-dimensional real spaces with absolute and symmetric norm. This allows us to compute the numerical index of the two-dimensional real $L_p$-space for $3/2\leq p\leq 3$.

Index of symmetry and topological classification of asymmetric normed spaces

Let X, Y be asymmetric normed spaces and Lc(X, Y) the convex cone of all linear continuous operators from X to Y. It is known that in general, Lc(X, Y) is not a vector space. The aim of this note is to prove, using the Baire category theorem, that if Lc(X, Y) is a vector space for some asymmetric normed space Y , then X is isomorphic to its associated normed space (the converse is true for every asymmetric normed space Y and is easy to establish). For this, we introduce an index of symmetry of the space X denoted c(X) $\in$ [0, 1] and we give the link between the index c(X) and the fact that L…

论算子的Davis-Wielandt壳与赋范线性空间的Davis-Wielandt指数

On the Davis-Wielandt shell of an operator and the Davis-Wielandt index of a normed linear space

该研究针对赋范线性空间上算子的Davis-Wielandt壳与半径展开，证明修正后的Davis-Wielandt半径可定义与通常算子范数等价的范数，引入Davis-Wielandt指数并给出特定及一般多面体Banach空间下的计算与估计方法。

连续函数空间的Szlenk指标的一个简短计算

A short calculation of the Szlenk index of spaces of continuous functions

本文利用Grasberg范数，对连续函数空间$C(K)$的Szlenk指标给出了一个简短的计算方法。

On joint numerical radius of operators and joint numerical index of a Banach space

Generalizing the notion of numerical range and numerical radius of an operator on a Banach space, we introduce the notion of joint numerical range and joint numerical radius of tuple of operators on a Banach space. We study the convexity of the joint numerical range. We show that the joint numerical radius defines a norm if and only if the numerical radius defines a norm on the corresponding space. Then we prove that on a finite-dimensional Banach space, the joint numerical radius can be retrieved from the extreme points. Furthermore, we introduce a notion of joint numerical index of a Banach …

Tsirelson型空间的$\ell ^{1}$ -指标

The $\ell ^{1}$-index of Tsirelson type spaces

如果α和β是可数序数，使得β \neq 0，则用\tilde{T}_{α,β}表示$c_{00}$关于隐式定义的范数的完备化||x|| = max{||x||_{ c_{0} }，1/2 sup \sum_{i=1}^{j}|| E_{i} x||}，其中上确界在所有有限子集E_{1}，.上取，$\mathbb{N}$的E_{j}，使得$E_{1}<...<E_{j}$和{min E_{1}，.，min E_{j} } \in S_β。证明了\tilde{T}_{α,β}的Bourgain $\ell^{1}$ -指数为ω^{α+β.ω}.特别地，如果α=ω^{α_{1}}。m_{1} +.+ω^{α_{n}}。若α_{n}不是极限序数，则存在\ell^{1} -指数为ω^α的Banach空间.