L^1(μ)上的强Dunford—Pettis算子的特征

Characteristics of strongly Dunford—Pettis operators on L^1(μ)

设(X,∑,μ)是一个σ-有限测度空间,讨论了L^1(μ)上强D-P算子的序性质,指出从L^1(μ)到c_0上的强D-P算子是弱紧的当且仅当它是紧的.刻画了L^1(μ)→c_0上D-P算子,强D-P算子、弱紧算子和紧算子之间的关系.

Let(X,E,μ)be a σ-finite measurable space,the order property of strongly D-P operators is studied.An operator T:L^1(μ)→C_o is a strongly D-P operator T is weakly Compact iff T is compact.The relationship of compact operators,weakly compact operator,D-P operators and strongly D-P operators are given.