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Bul. Acad. Ştiinţe Repub. Mold. Mat., 2014, Number 2, Pages 74–84 (Mi basm357)  

Research articles

A semi-isometric isomorphism on a ring of matrices

Svetlana Aleschenko

Tiraspol State University, str. Iablochkin 5, Chisinau MD-2069, Moldova

Abstract: Let $(R,\xi)$ be a pseudonormed ring and $R_n$ be a ring of matrices over the ring $R$. We prove that if $1\leq\gamma,\sigma\leq\infty$ and $\frac 1\gamma+\frac1\sigma\geq1$, then the function $\eta_{\xi,\gamma,\sigma}$ is a pseudonorm on the ring $R_n$. Let now $\varphi\colon(R,\xi)\to(\overline R,\overline\xi)$ be a semi-isometric isomorphism of pseudonormed rings. We prove that $\Phi\colon(R_n,\eta_{\xi,\gamma,\sigma})\to(\overline R_n,\eta_{\overline\xi,\gamma,\sigma})$ is a semi-isometric isomorphism too for all $1\leq\gamma,\sigma\leq\infty$ such that $\frac1\gamma+\frac1\sigma\ge1$.

Keywords and phrases: pseudonormed rings, quotient rings, ring of matrices, isometric homomorphism, semi-isometric isomorphism, canonical homomorphism.

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Document Type: Article
MSC: 16W60, 13A18
Received: 05.04.2014
Language: English

Citation: Svetlana Aleschenko, “A semi-isometric isomorphism on a ring of matrices”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2014, no. 2, 74–84

Citation in format AMSBIB
\Bibitem{Ale14}
\by Svetlana~Aleschenko
\paper A~semi-isometric isomorphism on a~ring of matrices
\jour Bul. Acad. \c Stiin\c te Repub. Mold. Mat.
\yr 2014
\issue 2
\pages 74--84
\mathnet{http://mi.mathnet.ru/basm357}


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