Derivations, local derivations and atomic boolean subspace lattices
Derivations, local derivations and atomic boolean subspace lattices
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DOI：
10.1017/s0004972700040314
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发表时间：
2002-12
影响因子：
0.7
通讯作者：
Pengtong Li;Ji-pu Ma
中科院分区：
文献类型：
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作者：
Pengtong Li;Ji-pu Ma
让ℒ原子布尔子空间晶格在巴拿赫空间X在这篇文章中,我们证明如果ℳ理想Algℒ然后每个派生δAlgℒℳ必然quasi-spatial,也就是说,存在一个人口定义封闭线性算子T:𝒟(T)⊆与其域𝒟→X (T)不变在Algℒ的每一个元素,这样δ(a) X = X (TA -在)每一个∈Algℒ每个X∈𝒟(T)。同时，如果∈(X)是一个algu -模，则证明了从algu -到的每一个局部推导都是一个必要的推导。特别地，每一个由Alg￣到y (X)的局部导数都是一个导数，而每一个由Alg￣到其自身的局部导数都是一个准空间导数。
Let ℒ be an atomic Boolean subspace lattice on a Banach space X. In this paper, we prove that if ℳ is an ideal of Alg ℒ then every derivation δ from Alg ℒ into ℳ is necessarily quasi-spatial, that is, there exists a densely defined closed linear operator T: 𝒟(T) ⊆ X → X with its domain 𝒟(T) invariant under every element of Alg ℒ, such that δ(A) x = (TA – AT) x for every A ∈ Alg ℒ and every x ∈ 𝒟(T). Also, if ℳ ⊆ ℬ(X) is an Alg ℒ-module then it is shown that every local derivation from Alg ℒ into ℳ is necessary a derivation. In particular, every local derivation from Alg ℒ into ℬ(X) is a derivation and every local derivation from Alg ℒ into itself is a quasi-spatial derivation.