Perturbation of the Wigner equation in inner product C*-modules (CROSBI ID 146277)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Podaci o odgovornosti
Chmielinski, Jacek ; Ilišević, Dijana ; Sal Moslehian, Mohammad ; Sadeghi, Ghadir
engleski
Perturbation of the Wigner equation in inner product C*-modules
Let $\A$ be a $C^*$-subalgebra of a von Neumann algebra $\B$. Let $\M$ and $\N$ be inner product modules over $\A$ and $\B$, respectively. Under some assumptions we show that for each mapping $f\colon{; ; ; \mathcal M}; ; ; \to {; ; ; \mathcal N}; ; ; $ satisfying $$\|\, |\ip{; ; ; f(x)}; ; ; {; ; ; f(y)}; ; ; |-|\ip{; ; ; x}; ; ; {; ; ; y}; ; ; |\, \|\leq\varphi(x, y)\qquad (x, y\in{; ; ; \mathcal M}; ; ; ), $$ where $\varphi$ is a control function, there exists a solution $I\colon{; ; ; \mathcal M}; ; ; \to {; ; ; \mathcal N}; ; ; $ of the Wigner equation $$|\ip{; ; ; I(x)}; ; ; {; ; ; I(y)}; ; ; |=|\ip{; ; ; x}; ; ; {; ; ; y}; ; ; |\qquad (x, y \in {; ; ; \mathcal M}; ; ; )$$ such that $$ \|f(x)-I(x)\|\leq\sqrt{; ; ; \varphi(x, x)}; ; ; \qquad (x\in {; ; ; \mathcal M}; ; ; ). $$
Wigner equation ; C*-modules
nije evidentirano
nije evidentirano
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Podaci o izdanju
49 (3)
2008.
33519
8
objavljeno
0022-2488
1089-7658
10.1063/1.2898486