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APPROXIMATELY C*-INNER PRODUCT PRESERVING MAPPINGS

Chmielinski, Jacek   (INSTITUTE OF MATHEMATICS PEDAGOGICAL UNIVERSITY OF CRACOW  ); Moslehian, Mohammad Sal   (DEPARTMENT OF MATHEMATICS FERDOWSI UNIVERSITY OF MASHHADUU0015728  );
  • 초록

    A mapping f : $M{\rightarrow}N$ between Hilbert $C^*$ -modules approximately preserves the inner product if $$\parallel /TEX> f(x),\;f(y) - /TEX> x,y \parallel\leq\varphi(x,y)$$ 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.


  • 주제어

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

  • 참고문헌 (26)

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