非紧距离空间上的Lipschitz-α算子空间

Lipschitz-α operator spaces on non-compact metric space

引入了由非紧距离空间(D,d)到一般Banach空间Y中的Lipschitz-α算子以及相应的算子空间Lα(D,Y)和lα(D,Y),证明了Lipschitz-α算子空间Lα(D,Y)与lα(D,Y)∩Lα(D,Y)关于范数‖T‖α,e=‖Te‖+Lα(T)是Banach空间,并讨论了(lBα(D,Y),‖.‖α,e)、(LBα(D,Y),‖.‖α,e)及(Lα(D,Y),‖.‖α,e)之间的关系.

In this paper, let （D,d） be a given non-compact metric Space, Y be a Banach space. Operator spaces Lα（D,Y）and lα（D,Y）, consisting of big Lipschitz-α operators and of little Lipschitz-α operators from D into Y, respectively, are introduced and discussed. It is proved that Lα（D,Y）and lα（D,Y） ∩Lα（D,Y） are Banach spaces with respect to the norm ‖T‖α,e=‖Te‖＋Lα（T） And, the inclusion relationships between these spaces arediscussed.