This article presents a novel method to prove that： let E be an AM-space and if dim E ≥ 3, then there does not exist any odd subtractive.isometric mapping from the unit sphere S（E） into S[L（Ω, μ）]. In particul...This article presents a novel method to prove that： let E be an AM-space and if dim E ≥ 3, then there does not exist any odd subtractive.isometric mapping from the unit sphere S（E） into S[L（Ω, μ）]. In particular, there does not exist any real linear isometry from E into L（Ω, μ）.展开更多
Let E and F be Banach lattices. It is known that if every continuous linear operator from E into F is regular, then, under some mild assumptions on E or F, either E is lattice isomorphic to an AL-space or F is lattice...Let E and F be Banach lattices. It is known that if every continuous linear operator from E into F is regular, then, under some mild assumptions on E or F, either E is lattice isomorphic to an AL-space or F is lattice isomorphic to an AM-space. Here we present a characterization on an AL-space E such that every bounded linear operator from E into a Banach lattice is regular. A counterexample is also provided, which shows that the results are unexpected even if the domain is an AL-space or the range space is an AM-space.展开更多
We first characterize the range spaces F for which {T＇：T∈K（E,F）}=K（F＇,E＇） holds for all Banach spaces E. Then we present some sufficient conditions for the equality T＇=T＇. Some related results are also incl...We first characterize the range spaces F for which {T＇：T∈K（E,F）}=K（F＇,E＇） holds for all Banach spaces E. Then we present some sufficient conditions for the equality T＇=T＇. Some related results are also included.展开更多
基金This study is supported by the National Natural Science Foundation of China (10571090)the Research Fund for the Doctoral Program of Higher Education (20060055010)
文摘This article presents a novel method to prove that： let E be an AM-space and if dim E ≥ 3, then there does not exist any odd subtractive.isometric mapping from the unit sphere S（E） into S[L（Ω, μ）]. In particular, there does not exist any real linear isometry from E into L（Ω, μ）.
文摘Let E and F be Banach lattices. It is known that if every continuous linear operator from E into F is regular, then, under some mild assumptions on E or F, either E is lattice isomorphic to an AL-space or F is lattice isomorphic to an AM-space. Here we present a characterization on an AL-space E such that every bounded linear operator from E into a Banach lattice is regular. A counterexample is also provided, which shows that the results are unexpected even if the domain is an AL-space or the range space is an AM-space.
基金The Special Topic Research Project of Southwest Jiaotong University (SWJTU09ZT36)
文摘We first characterize the range spaces F for which {T＇：T∈K（E,F）}=K（F＇,E＇） holds for all Banach spaces E. Then we present some sufficient conditions for the equality T＇=T＇. Some related results are also included.
