TY - JOUR
ID - 5330
TI - $C^*$-metric spaces
JO - International Journal of Nonlinear Analysis and Applications
JA - IJNAA
LA - en
SN -
AU - Mowlavi, Mahdi
AU - Mirzavaziri, Madjid
AU - Mardanbeigi, Mohammadreza
AD - Department of Mathematics,Faculty of Science,Science and Research Branch Islamic Azad University,Tehran , Iran.
AD - Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad
AD - Department of Mathematics, Faculty of Science, Science and Research Branch Islamic Azad University, Tehran, Iran
Y1 - 2021
PY - 2021
VL - 12
IS - 2
SP - 1991
EP - 1996
KW - $C^*$-algebra
KW - $C^*$-metric space
KW - allowance set
KW - downward/upward directed set
KW - positive elements
DO - 10.22075/ijnaa.2020.20839.2205
N2 - The purpose of this article is to introduce the notion of an $\mathfrak{A}$-meter, as an operator-valued distance mapping on a set $X$ and investigating the theory of $\mathfrak{A}$-metric spaces, where $\mathfrak{A}$ is a noncommutative $C^*$-algebra. We demonstrate that each metric space may be seen as an $\mathfrak{A}$-metric space and that every $\mathfrak{A}$-metric space $(X,\delta)$ can be regarded as a topological space $(X,\tau_{\delta})$.
UR - https://ijnaa.semnan.ac.ir/article_5330.html
L1 - https://ijnaa.semnan.ac.ir/article_5330_1ba8b26200a89ba63930f1ea47b3263b.pdf
ER -