论文标题
标准运算符代数的派生，本地和2个本地派生
Derivations, local and 2-local derivations of standard operator algebras
论文作者
论文摘要
令X为Field F（R或C）上的Banach空间。用b（x）表示x和f（x）上所有有界线性运算符的集合。我们简短地证明了一个众所周知的结果，即从A到B（X）的每个派生都内部。还有另一个经典结果，即B（x）上的每个局部派生都是派生。我们通过证明从A到B（X）的每个局部推导都是派生来扩展结果。基于这两个结果，我们证明了从A到B（X）的每个2个局部派生是一个派生。
Let X be a Banach space over field F (R or C). Denote by B(X) the set of all bounded linear operators on X and by F(X) the set of all finite rank operators on X. A subalgebra A of B(X) is called a standard operator algebra if A contain F(X). We give a brief proof of a well-known result that every derivation from A into B(X) is inner. There is another classical result that every local derivation on B(X) is a derivation. We extend the result by proving that every local derivation from A into B(X) is a derivation. Based on these two results, we prove that every 2-local derivation from A into B(X) is a derivation.
