算子权移位的紧性,正权和C_(αβ) 分类

Compactness, Positive Weights and C_(αβ) Classification of Operator Weighted Shifts

给出复可分Hilbert空间上任意重的算子权移位是紧算子的充要条件,重新证明了每个算子权移位酉等价于一个正算子权移位并讨论了算子权移位S～{Wk}与T～{|Wk|}的关系,给出了压缩的任意重算子权移位的Cαβ分类的充要条件.

The sufficient and necessary condition is given for any multiple operator weighted shifts on separable complex Hilbert spaces to be compact operators, then the relations between operator weighted shifts S～{W_k} and T～{|W_k|} are discussed, and finally C_(αβ) classification of contracted any multiple operator weighted shifts are described.