Title : ( APPROXIMATELY C¤-INNER PRODUCT PRESERVING MAPPINGS )
Authors: Jacek Chmielinski , Mohammad Sal Moslehian ,
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Abstract
A mapping f : M → N between Hilbert C∗-modules approximately preserves the inner product if ∥⟨f(x), f(y)⟩ − ⟨x, y⟩∥ ≤ φ(x, y) for an appropriate control function φ(x, y) and all x, y ∈ 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.
Keywords
, Hilbert C∗-module, Hyers–Ulam–Rassias stability, superstability, orthogonality equation, asymptotic behavior.
@article{paperid:1006979,
author = {Jacek Chmielinski and Sal Moslehian, Mohammad},
title = {APPROXIMATELY C¤-INNER PRODUCT PRESERVING MAPPINGS},
journal = {Bulletin of Korean Chemical Society},
year = {2008},
volume = {45},
number = {1},
month = {January},
issn = {0253-2964},
pages = {157--167},
numpages = {10},
keywords = {Hilbert C∗-module; Hyers–Ulam–Rassias stability; superstability;
orthogonality equation; asymptotic behavior.},
}
%0 Journal Article
%T APPROXIMATELY C¤-INNER PRODUCT PRESERVING MAPPINGS
%A Jacek Chmielinski
%A Sal Moslehian, Mohammad
%J Bulletin of Korean Chemical Society
%@ 0253-2964
%D 2008
