本课题我们将研究以下几个问题：.1) 设A是单的有单位的实秩零的C*-代数. 则A是否由A中的投影线性生成？.2) 设A是单的有单位的顺从的C*-代数. 则由A中的投影全体线性生成的子空间在A中是否是范数闭的？.3) 任意C*-代数上的2-局部导子是否都是导子？.4) Nest代数、CSL代数等一些子空间代数上的2-局部导子问题..5) 任意von Neumann代数上的弱-2-局部导子是否都是导子？

In this project, we will study the following several problems:.1) Suppose that A is a unital, simple, real rank zero C*-algebra. Must the linear span of the projections coincide with A?.2) Suppose that A is a unital, simple, amenable C*-algebra. Is the linear span of the projections in A closed in the norm topology?.3) Is every 2-local derivation on a general C*-algebra a derivation?.4) 2-local derivations on some subspace lattice algebras, such as Nest algebras, CSL algebras and so on..5) Is every weak-2-local derivation on an arbitrary von Neumann algebra a derivation?