In this paper we study the three new asymptotic-norming properties which are called locally asymptotic-norming property k,k=Ⅰ, Ⅱ,Ⅲ, and discuss the relationship between the locally asymptotic-norming property and t...In this paper we study the three new asymptotic-norming properties which are called locally asymptotic-norming property k,k=Ⅰ, Ⅱ,Ⅲ, and discuss the relationship between the locally asymptotic-norming property and the Kadec Property.展开更多
The relationship between some smoothness and weak asymptotic-norming properties of dual Banach space X is studied. The main results are the following. Suppose that X is weakly sequential complete Banach space, then X...The relationship between some smoothness and weak asymptotic-norming properties of dual Banach space X is studied. The main results are the following. Suppose that X is weakly sequential complete Banach space, then X is Frechet differentiable if and only if X has B （X）- ANP -I, X is quasi-Frechet differentiable if and only if X has B（X）- ANP -H and X is very smooth if and only if X has B（X）- ANP -Ⅱ. A new local asymptotic-norming property is also introduced, and the relationship among this one and other local asymptotic-norming properties and some topological properties is discussed. In addition, this paper gives a negative answer to the open question raised by Hu and Lin in Bull. Austral. Math. Soc,45,1992.展开更多
文摘In this paper we study the three new asymptotic-norming properties which are called locally asymptotic-norming property k,k=Ⅰ, Ⅱ,Ⅲ, and discuss the relationship between the locally asymptotic-norming property and the Kadec Property.
基金National Natural Science Foundation of China(10671118) the Natural Science Foundation of Shanghai Education Committee (06NZ016)
文摘The relationship between some smoothness and weak asymptotic-norming properties of dual Banach space X is studied. The main results are the following. Suppose that X is weakly sequential complete Banach space, then X is Frechet differentiable if and only if X has B （X）- ANP -I, X is quasi-Frechet differentiable if and only if X has B（X）- ANP -H and X is very smooth if and only if X has B（X）- ANP -Ⅱ. A new local asymptotic-norming property is also introduced, and the relationship among this one and other local asymptotic-norming properties and some topological properties is discussed. In addition, this paper gives a negative answer to the open question raised by Hu and Lin in Bull. Austral. Math. Soc,45,1992.
