Property AUB is the notion in metric geometry which has applications in higher index problems.In this paper,the permanence property of property AUB of metric spaces under large scale decompositions of finite depth is ...Property AUB is the notion in metric geometry which has applications in higher index problems.In this paper,the permanence property of property AUB of metric spaces under large scale decompositions of finite depth is proved.展开更多
设X为Banach空间,记U(X)={x∈X:‖x‖≤1}。V.I.Istratescu引入了下面两个概念。Banach空间Z叫做k一致凸的,如果对每个ε>0,存在δ(ε)>0,当x_1,…,x_k,y_1,…,y_k为U(X)中的元素且sum from i=1 to k(‖x_i-y_i‖≥ε)时,有‖x_1+...设X为Banach空间,记U(X)={x∈X:‖x‖≤1}。V.I.Istratescu引入了下面两个概念。Banach空间Z叫做k一致凸的,如果对每个ε>0,存在δ(ε)>0,当x_1,…,x_k,y_1,…,y_k为U(X)中的元素且sum from i=1 to k(‖x_i-y_i‖≥ε)时,有‖x_1+…+x_k+y_1+…y_k‖≤2k(1-δ(ε))。X叫做k一致光滑的,如果当τ→0时,ρ_k(τ)/τ→0,其中ρ_k,x(τ)规定为 2kp_k,x(τ)=sup{sum from i=1 to k(‖x+τy_i‖+‖x-τy_i‖)-2k:‖x‖=‖y_i‖=1 i=1,…k,} 本文证明上述k一致凸性等价于一致凸性,并且X为k一致光滑的当且仅当X为一致光滑的,因此这两个概念都不是新的概念。展开更多
After studying in a previous work the smoothness of the space where dr- measF0 〉 O, with p（.） E C（~） and p（x） 〉 1 for all x E , the authors study in this paper the strict and uniform convexity as well as some ...After studying in a previous work the smoothness of the space where dr- measF0 〉 O, with p（.） E C（~） and p（x） 〉 1 for all x E , the authors study in this paper the strict and uniform convexity as well as some special properties of duality mappings defined on the same space. The results obtained in this direction are used for proving existence results for operator equations having the form Ju = Niu, where J is a duality mapping on Uro corresponding to the gauge function ~, and Nf is the Nemytskij operator generated by a Caratheodory function f satisfying an appropriate growth condition ensuring that Nf may be viewed as acting from Ur0 into its dual.展开更多
基金National Natural Science Foundations of China(No.10901033,No.10971023)Shanghai Pujiang Project,China(No.08PJ1400600)+1 种基金Shanghai Shuguang Project,China(No.07SG38)the Fundamental Research Funds for the Central Universities of China
文摘Property AUB is the notion in metric geometry which has applications in higher index problems.In this paper,the permanence property of property AUB of metric spaces under large scale decompositions of finite depth is proved.
文摘设X为Banach空间,记U(X)={x∈X:‖x‖≤1}。V.I.Istratescu引入了下面两个概念。Banach空间Z叫做k一致凸的,如果对每个ε>0,存在δ(ε)>0,当x_1,…,x_k,y_1,…,y_k为U(X)中的元素且sum from i=1 to k(‖x_i-y_i‖≥ε)时,有‖x_1+…+x_k+y_1+…y_k‖≤2k(1-δ(ε))。X叫做k一致光滑的,如果当τ→0时,ρ_k(τ)/τ→0,其中ρ_k,x(τ)规定为 2kp_k,x(τ)=sup{sum from i=1 to k(‖x+τy_i‖+‖x-τy_i‖)-2k:‖x‖=‖y_i‖=1 i=1,…k,} 本文证明上述k一致凸性等价于一致凸性,并且X为k一致光滑的当且仅当X为一致光滑的,因此这两个概念都不是新的概念。
文摘After studying in a previous work the smoothness of the space where dr- measF0 〉 O, with p（.） E C（~） and p（x） 〉 1 for all x E , the authors study in this paper the strict and uniform convexity as well as some special properties of duality mappings defined on the same space. The results obtained in this direction are used for proving existence results for operator equations having the form Ju = Niu, where J is a duality mapping on Uro corresponding to the gauge function ~, and Nf is the Nemytskij operator generated by a Caratheodory function f satisfying an appropriate growth condition ensuring that Nf may be viewed as acting from Ur0 into its dual.
