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arXiv · 1901.02394

On Completion of \textit{C}*-algebra-valued metric spaces

Wanchai Tapanyo·Wachiraphong Ratiphaphongthon·Areerat Arunchai
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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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Wanchai Tapanyo, Wachiraphong Ratiphaphongthon, Areerat Arunchai. 2019-01-08. On Completion of \textit{C}*-algebra-valued metric spaces. https://arxiv.org/abs/1901.02394

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