非紧距离空间上的有界Lipschitz-α算子

Bounded Lipschitz-α Operators on Non-Compact Metric Space

引入了由非紧距离空间(X,d)到一般Banach空间Z上的有界Lipschitz-α算子及相应的算子空间,证明了算子空间LαB(X,Z)和L0α(X,Z)分别关于某些范数构成Banach空间,并证明了在一定条件下Banach空间LαB(X,Z)等距同构到某一Banach空间L0α(Y,Z).

Bounded Lipschitz-α Operators from （ X, d ） into Z and relative operator spaces are introduced. It is proved that LB^α（X,Z） and L0^α（X, Z） are Banach spaces with respect to some norms respectively. It is also shown that L0^α（X,Z） is isometricly isomorphic to some LB^α（Y,Z） under certain conditions.