二阶算子矩阵代数中的全可导点

All-derivable Point in 2×2 Operator Matrices

设H是复Hilbert空间,A是B(H)上的一个算子代数。如果每一个在Z点可导且在强算子拓扑下连续的线性映射是个导子,则称算子Z是A的关于强算子拓扑的全可导点。作者证明:E=[V000](V是可逆算子)是二阶算子矩阵代数的关于强算子拓扑的全可导点.

Let H be a complex Hilbert and A be an operator algebra on B（H）.We say that an element Z ∈A is an all-derivable point of A for the majorant operator topology if,every majorant operator topology continuous derivable linear mapping φ at Z is a derivation.We show in this paper that E=[^00V0]（V is an invertible operator） is an all-derivable point for the majorant operator topology of 2×2 operator matrix algebra.