非紧距离空间上的Lipschitz-α算子

Lipschitz-α operators on non-compact metric space

引入大Lipschitz-a*数和小Lipschitz-a*数以及算子空间L a*(X,Y),La*β(X,Y),La*0(X,Y),la*(X,Y),la*β(X,Y),证明了La*0(X,Y)关于范数‖·‖l构成Banach算子空间,Laβ*(X,Y)关于范数‖·‖a*,‖·‖max构成Banach空间,进一步证明它们各自构成Banach代数并讨论了由有界算子空间构成的Banach代数(La0*(X,Y),‖·‖a*)与有界算子空间构成的Banach代数(La*β(X,Y),‖·‖a*)之间的关系.

Large number Lipschitz-a＊, small number Lipschitz-a＊ and operator spacesL^α＊（X,Y）,Lβ^α＊（X,Y）,L0^α＊（X,Y）,l^α＊（X,Y）,and lβ^α＊（X,Y）,are introduced. It is proved that L0^α＊（X,Y） and Lβ^α＊（X,Y） are Banach space with respect to somenorms respectively. Further, their constitutes Banach algebra is shown and the relationship between Banach algebra （L0^α＊（X,Y）,‖·‖a＊）and（Lβ^α＊（X,Y）,‖·‖a＊）is discussed which is composed by the bounded operator space.