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 $d(z)=z+z+dz$ 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: https://doi.org/10.18514/MMN.2015.1108


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