• Chmielinski, Jacek ;
  • Moslehian, Mohammad Sal
  • Published : 2008.02.29


A mapping f : $M{\rightarrow}N$ between Hilbert $C^*$-modules approximately preserves the inner product if $$\parallel<f(x),\;f(y)>-<x,y>\parallel\leq\varphi(x,y)$$ for an appropriate control function $\varphi(x,y)$ and all x, y $\in$ M. In this paper, we extend some results concerning the stability of the orthogonality equation to the framework of Hilbert $C^*$-modules on more general restricted domains. In particular, we investigate some asymptotic behavior and the Hyers-Ulam-Rassias stability of the orthogonality equation.


Hilbert $C^*$-module;Hyers-Ulam-Rassias stability;superstability;orthogonality equation;asymptotic behavior


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