原子Boolean格代数的导子

Derivations of Atomic Boolean Lattice Algebras

设是Banach空间X上的原子Boolean子空间格，δ是alg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∈alg）在T的定义域（T）上成立．另外，如果还是一个有限格，并且对的任一原子L，L＋L＇闭，则δ是连续的和内的．

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