In this article, we study the preservation properties of （Silov） boundary of mul-tiplieative subgroups in C（X） spaces for non-surjective norm-preserving multiplieative maps.We also show a sufficient condition for ...In this article, we study the preservation properties of （Silov） boundary of mul-tiplieative subgroups in C（X） spaces for non-surjective norm-preserving multiplieative maps.We also show a sufficient condition for surjective maps between groups of positive continuousfunctions to be a composition operator.展开更多
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supported in part by the NSFC(11671314)the Foundation of Hubei Provincial Department of Education(Q20161602)+1 种基金supported in part by the NSF-DMS(1200370)the NSFC(11628102)
文摘In this article, we study the preservation properties of （Silov） boundary of mul-tiplieative subgroups in C（X） spaces for non-surjective norm-preserving multiplieative maps.We also show a sufficient condition for surjective maps between groups of positive continuousfunctions to be a composition operator.
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)).
