IJPAM: Volume 106, No. 1 (2016)

ON HILBERT $C^*$-modules

Sayed Khalil Ekrami$^1$, Madjid Mirzavaziri$^2$
$^1$Department of Mathematics
Payame Noor University
P.O. Box 19395-3697, Tehran, IRAN
$^2$Department of Pure Mathematics
Ferdowsi University of Mashhad
P. O. Box 1159, Mashhad 91775, IRAN

Abstract. Let $ \mathcal{H} $ be a Hilbert $C^*$-module over a unital $C^*$-algebra $ \mathcal{A} $. In this paper, we find the general form of the mappings $ T:\mathcal{H} \rightarrow \mathcal{H} $ satisfing \begin{equation*}
2\langle T(x),T(y) \rangle = \langle T(x),y \rangle + \langle x,T(y) \rangle \quad (x,y\in \mathcal{H}),
\end{equation*} as adjointable (bounded) $ \mathcal{A} $-linear operators. The generalized Hyers-Ulam stability of the functional equation is discussed.

Received: September 6, 2015

AMS Subject Classification: 39B52, 46L08

Key Words and Phrases: Hilbert $C^*$-module, $C^*$-algebra, $ \mathcal{A} $-linear mapping

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DOI: 10.12732/ijpam.v106i1.15 How to cite this paper?

International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 106
Issue: 1
Pages: 199 - 212

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