摘要
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.
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.
