We express the set of exposed points in terms of rotund points and non-smooth points.As long as we have Banach spaces each time＂bigger＂,we consider sets of non-smooth points each time＂smaller＂.
In this paper, we study the extension of isometries between the unit spheresof some Banach spaces E and the spaces C(Ω). We obtain that if the set sm.S_1(E) of all smoothpoints of the unit sphere S_1(E) is dense in S...In this paper, we study the extension of isometries between the unit spheresof some Banach spaces E and the spaces C(Ω). We obtain that if the set sm.S_1(E) of all smoothpoints of the unit sphere S_1(E) is dense in S_1(E), then under some condition, every surjectiveisometry V_0 from S_1(E) onto S_1(C(Ω)) can be extended to be a real linearly isometric map V of Eonto C(Ω). From this result we also obtain some corollaries. This is the first time we study thisproblem on different typical spaces, and the method of proof is also very different too.展开更多
In this article,we use some analytic and geometric characters of the smooth points in a sphere to study the isometric extension problem in the separable or reflexive real Banach spaces.We obtain that under some condit...In this article,we use some analytic and geometric characters of the smooth points in a sphere to study the isometric extension problem in the separable or reflexive real Banach spaces.We obtain that under some condition the answer to this problem is affirmative.展开更多
文摘We express the set of exposed points in terms of rotund points and non-smooth points.As long as we have Banach spaces each time＂bigger＂,we consider sets of non-smooth points each time＂smaller＂.
文摘In this paper, we study the extension of isometries between the unit spheresof some Banach spaces E and the spaces C(Ω). We obtain that if the set sm.S_1(E) of all smoothpoints of the unit sphere S_1(E) is dense in S_1(E), then under some condition, every surjectiveisometry V_0 from S_1(E) onto S_1(C(Ω)) can be extended to be a real linearly isometric map V of Eonto C(Ω). From this result we also obtain some corollaries. This is the first time we study thisproblem on different typical spaces, and the method of proof is also very different too.
基金Supported by National Natural Science Foundation of China(Grant No.11371201)
文摘In this article,we use some analytic and geometric characters of the smooth points in a sphere to study the isometric extension problem in the separable or reflexive real Banach spaces.We obtain that under some condition the answer to this problem is affirmative.
基金Supported by National Natural Science Foundation of China （Grant No. 10871101） and the Research Fund for the Doctoral Program of Higher Education （Grant No. 20060055010）
文摘In two real Banach spaces, we shall present two conditions, under one of which each nonexpansive mapping must be an isometry.
