原子Boolean格代数的导子

Derivations of Atomic Boolean Lattice Algebras

中文关键词:  原子Boolean子空间格  导子

英文关键词:atomic Boolean subspace lattice  derivation

中文摘要:

      设L是Banach空间X上的原子Boolean子空间格，δ是algL的任一导子，则存在X中的一个稠定线性算子T，使得δ（A）＝AT—TA（A∈algL）在T的定义域D（T）上成立．另外，如果L还是一个有限格，并且对L的任一原子L，L＋L＇闭，则δ是连续的和内的．

英文摘要:

      Let L be an atomic Boolean subspace lattice in Banach space X and δ a derivation of algL. Then there exists a densely defined operator T on X such that δ(A)=AT-TA holds on the domain D(T) of T for every A∈algL. In addition, if L is finite and L+L' is closed for every atom L of L, then δ is continuous and inner.