On Completion of C*-algebra-valued metric spaces

2019/01/08 by Tapanyo, Wanchai, Ratiphaphongthon, Wachiraphong, Arunchai, Areerat
#46B99 #46L99 #54E50 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1901.02394

Abstract

The concept of a C *-algebra-valued metric space was introduced in 2014. It is a generalization of a metric space by replacing the set of real numbers by a C *-algebra. In this paper, we show that C *-algebra-valued metric spaces are cone metric spaces in some point of view which is useful to extend results of the cone case to C *-algebra-valued metric spaces. Then the completion theorem of C *-algebra-valued metric spaces is obtained. Moreover, the completion theorem of C *-algebra-valued normed spaces is verified and the connection with Hilbert C *-modules, generalized inner product spaces, is also provided.

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