MMN-1108
Kinds of derivations on Hilbert $C^*$-modules and their operator algebras
Hossein Saidi; Ali Reza Janfada; Madjid Mirzavaziri;Abstract
Let $\mathcal{M}$ be a Hilbert $C^*$-module. A linear mapping
$d:\mathcal{M}\rightarrow\mathcal{M}$ is called a derivation if
$d(<x,y>z)=<dx,y>z+<x,dy>z+<x,y>dz$ for all $x,y,z\in\mathcal{M}$.
We give some results for derivations and automatic continuity of
them on $\mathcal{M}$. Also, we will characterize generalized
derivations and strong higher derivations on the algebra of compact
operators and adjointable operators of Hilbert $C^*$-modules,
respectively.
Vol. 16 (2015), No. 1, pp. 453-461
DOI: 10.18514/MMN.2015.1108