Generalized Modulus of Smoothness in Banach Spaces - ZHAO Liang; WANG Wei-wei; ZHANG Xing (Journal of Harbin University of Science and Technology)
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.