Dynamical Systems Implemented by Isomorphic Groups of Unitaries

Mosadeq, Maysam

doi:10.22130/scma.2023.559758.1158

Document Type : Research Paper

Author

Maysam Mosadeq

Department of Mathematics, Larestan Branch, Islamic Azad University, Larestan, Iran.

https://doi.org/10.22130/scma.2023.559758.1158

Abstract

Let $\varphi:A\to B$ be an isomorphism of $C^*$-algebras and $I$ be an ideal of $A.$ Introducing the concepts of unitary equivalent and the implemented Finsler modules, we show that the $\frac{A}{I}$-module $\frac{E}{E_{I}}$ and the implemented $\frac{B}{\varphi(I)}$-module $\frac{F}{F_{\varphi(I)}}$ are unitary equivalent. We also, establish a one to one correspondence between the groups $U(E)$ and $U(F)$ of unitaries on full Finsler modules $E$ and $F,$ respectively. Finally, we explain regularized dynamical systems and apply the aforementioned one to one correspondenec to prove that each regularized dynamical system in $U(E)$ implements a regularized dynamical system in $U(F).$

Keywords

References

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Sahand Communications in Mathematical Analysis

Dynamical Systems Implemented by Isomorphic Groups of Unitaries

References

References

Articles in Press, Accepted Manuscript
Available Online from 12 March 2023

Dynamical Systems Implemented by Isomorphic Groups of Unitaries

References

References

Articles in Press, Accepted Manuscript Available Online from 12 March 2023

Articles in Press, Accepted Manuscript
Available Online from 12 March 2023