1) k-strongly extreme point
k-强端点
1.
In this paper, we prove that a k-extreme point(k-strongly extreme point) of the unit sphere in Banach spaces must be a(k+1)-extreme point((k+1)-strongly extreme point).
证明了Banach空间单位球面上的k-端点(k-强端点)必为(k+1)—端点((k+1)—强端点),给出了赋Luxemburg范数的Orlicz空间单位球k—端点(k—强端点)的判据,并据此得到了赋Luxemburg范数Orlicz空间是K严格凸和中点局部K一致凸的条件。
2) k-extreme point
k-端点
1.
In this paper, we prove that a k-extreme point(k-strongly extreme point) of the unit sphere in Banach spaces must be a(k+1)-extreme point((k+1)-strongly extreme point).
证明了Banach空间单位球面上的k-端点(k-强端点)必为(k+1)—端点((k+1)—强端点),给出了赋Luxemburg范数的Orlicz空间单位球k—端点(k—强端点)的判据,并据此得到了赋Luxemburg范数Orlicz空间是K严格凸和中点局部K一致凸的条件。
2.
This paper presents that a point in the unit sphere of X/M is k-extreme point of closed unit ball if every point on [x]∩S(X) is a k-extreme point of closed unit ball.
证明了商空间X/M单位球面上的点[x]为闭单位球的k-端点的充分条件是[x]与X的单位球面的交集中任一点均为闭单位球的k-端点,其中M是Banach空间X的可逼近子空间。
3.
Criteria for k-extreme points and k-strong extreme points of the unit ball in Orlicz function spaces with Orlicz norm is given.
给出了赋Orlicz范数的Orlicz函数空间单位球k-端点和k-强端点的判据,并据此方便地得到了赋Oricz范数Orlicz函数空间是K严格凸(KR)和中点局部K一致凸(MLKUR)的条
3) strongly extreme points
强端点
1.
For Orlicz-Bochner sequence spaces with Luxemburg norm,the (criteria) of the strongly extreme points and mid-point locally uniformly rotundity have been given.
给出了赋Luxemburg范数的Orlicz-Bochner序列空间强端点和中点局部一致凸的判别条件。
2.
Extreme points, strongly extreme points and nonsquareness are important geometric properties in Orlicz spaces, and they have close connections with convexity, flatness and reflexity.
端点、强端点及非方性是Orlicz空间中的重要的几何概念,它与凸性、平坦性和自反性有着紧密的联系。
4) Strong extreme point
强端点
1.
This article has proved that the strong extreme points f(Z)=I+B(n)Z￣n+B(n+1)Z￣(n+1)+…of P(△),must not have the following property;B(n)=B(n)and B(n)is an invertible opera-tor.
本文首先引进了单位园△上算子值解析函数族：Ｐ（△）＝｛ｆ（Ｚ），ｆ（Ｚ）＝Ｉ＋Ｂ（Ｉ）Ｚ＋Ｂ（２）Ｚ￣２＋…在△内解析，且Ｒｅｆ（Ｚ）＞０，Ｂ（ｎ）为Ｈｉｌｂｅｒｔ空间Ｈ上的正规算子，ｎ＝１，２…｝的强端点的概念，然后指出Ｐ（△）中形如Ｉ＋Ｂ（ｎ）Ｚ￣ｎ＋Ｂ（ｎ＋１）Ｚ￣（ｎ＋１）＋…的元素成Ｘ＿１Ｐ（△）的一个强端点的必要条件为Ｂ（ｎ）不是自伴可逆算子。
5) complex strongly extreme points
复强端点
6) strongly extreme point
强端点
1.
Extreme and strongly extreme points in Orlicz sequence spaces equipped with the generalized Orlicz norm
赋广义Orlicz范数的Orlicz序列空间的端点和强端点
2.
The criterion for strongly extreme points in the Orlicz function space with generalized Orlicz norm is given.
给出了赋广义Orlicz范数的Orlicz函数空间的强端点的判别准则,并据此得到了Orlicz函数空间关于广义Orlicz范数中点局部一致凸的条件。
补充资料：椐椐强强
1.相随貌。
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