Quasi-isometric embedding between $\ast$-algebras

Abstract

The concept of quasi-isometric embedding maps between $\ast$-algebras is introduced. We have obtained some basic results related to this notion and similar to quasi-isometric embedding maps on metric spaces, under some conditions, we give a necessary and sufficient condition on a $\ast$-homomorphism to be a quasi-isometric embedding between $\ast$-algebras.

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