Banach空间具有正规结构的判定条件

Generalized Modulus of Smoothness in Banach Spaces

为了研究Banach空间的几何常数,依据凸性模和光滑模的定义和性质,采用将光滑模推广到广义光滑模的方法来研究新常数。依据Lindenstrauss公式以及凸性模与光滑模的对偶关系,进一步研究广义光滑模与广义凸性模的的关系,不再局限于光滑模定义的条件,对新常数中的变量研究能够得出Banach空间具有的性质,从而给出了广义光滑模与广义凸性特征的一个关系,再通过广义光滑模与弱正交系数的关系,运用范数三角不等式,得出了Banach空间具有正规结构的充分条件。

In order to study the geometric constants of Banach space,a new method is extended to study new constants by means of extending the modulus of smoothness to the generalized smooth mode.On the basis of the Lindenstrauss formula and the duality between the modulus of convexity and modulus of smoothness,further study of generalized modulus of smoothness and generalized modulus of convexity and modulus of smoothness is no longer confined to the defined conditions,properties of the variables can be obtained in constant research of new space with Banach,which gives a relation between the generalized modulus of smoothness and generalized convex the characteristics.Through the relationship between generalized modulus of smoothness and weak orthogonal coefficients,by means of the norm of the triangle inequality,sufficient conditions are obtained for normal structure in Banach space.