Orlicz空间及其上的复合算子

Weighted composition operators in Orlicz spaces

讨论O rlicz空间上的复合算子C(其中∶X→X是非奇异变换)以及当u∈L∞时加权复合算子MuC的有界性、可逆性等问题,给出了一些等价刻划,同时讨论了O rlicz序列空间中的复合算子是等距算子的条件.

In this paper, some properties of composition operator Cτ and weighted composition operator MuCτ in Orlicz spaces are discussed （let τ be a nonsingular transform, u∈L^∞ ）. We give some necessary and sufficient conditions about boundedness, invertibility of these operators, and also discuss metric-preserving property of Cτ in Orlicz sequence spaces.