In this paper, we give four general results on linear extension of isometries between the unit spheres in β-normed spaces. These results improve the corresponding theorems in β-normed spaces.
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
文摘In this paper, we give four general results on linear extension of isometries between the unit spheres in β-normed spaces. These results improve the corresponding theorems in β-normed spaces.
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.
