For 1<p<∞,let S(Lp)+be the set of positive elements in L_(p) with norm one.Assume that V_(0):S(L_(p)(Ω_(1)))+→S(L_(p)(Ω_(2)))+is a surjective norm-additive map;that is,‖V_(0)(x)+V_(0)(y)‖=‖x+y‖,■x,y∈S(...For 1<p<∞,let S(Lp)+be the set of positive elements in L_(p) with norm one.Assume that V_(0):S(L_(p)(Ω_(1)))+→S(L_(p)(Ω_(2)))+is a surjective norm-additive map;that is,‖V_(0)(x)+V_(0)(y)‖=‖x+y‖,■x,y∈S(L_(p)(Ω_(1)))+.In this paper,we show that V_(0) can be extended to an isometry from L_(p)(Ω_(1))onto L_(p)(Ω_(2)).展开更多
基金partially supported by the NSF of China(11671314)partially supported by the NSF of China(12171251)。
文摘For 1<p<∞,let S(Lp)+be the set of positive elements in L_(p) with norm one.Assume that V_(0):S(L_(p)(Ω_(1)))+→S(L_(p)(Ω_(2)))+is a surjective norm-additive map;that is,‖V_(0)(x)+V_(0)(y)‖=‖x+y‖,■x,y∈S(L_(p)(Ω_(1)))+.In this paper,we show that V_(0) can be extended to an isometry from L_(p)(Ω_(1))onto L_(p)(Ω_(2)).
