HilbertC~＊─模中导子的自动连续性

AUTOMATIC CONTINUITY OF DERIVATIONS OF HILBERT C￣*-MODULE

本文首次引入ＨｉｌｂｅｒｔＣ＊－模中导子的概念，证明了ＨｉｌｂｅｒｔＣ＊－模的每个导子均是自动连续的。

Let A be a C*-algebra and let H be aHilbert C*-module over A,a linear map δfrom H to H is called a derivation of H if it satisfies the following condition: for every x,y. zin H. It has beeu proved that every derivation of a Hilbert C*-module over a C* algebra is automatic continous.