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$C^*$-metric spaces | ||
| International Journal of Nonlinear Analysis and Applications | ||
| دوره 12، شماره 2، بهمن 2021، صفحه 1991-1996 اصل مقاله (377.38 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2020.20839.2205 | ||
| نویسندگان | ||
| Mahdi Mowlavi1؛ Madjid Mirzavaziri* 2؛ Mohammadreza Mardanbeigi3 | ||
| 1Department of Mathematics,Faculty of Science,Science and Research Branch Islamic Azad University,Tehran , Iran. | ||
| 2Department of Pure Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad | ||
| 3Department of Mathematics, Faculty of Science, Science and Research Branch Islamic Azad University, Tehran, Iran | ||
| تاریخ دریافت: 20 تیر 1399، تاریخ پذیرش: 18 آذر 1399 | ||
| چکیده | ||
| 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 $(X,\tau_{\delta})$. | ||
| کلیدواژه‌ها | ||
| $C^*$-algebra؛ $C^*$-metric space؛ allowance set؛ downward/upward directed set؛ positive elements | ||
| مراجع | ||
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[1] J. Dixmier, C*-Algebras, Translated from the French by Francis Jellett, North-Holland Mathematical Library, Vol. 15. North-Holland Publishing Co., Amsterdam-New York-Oxford, 1977. [2] G. Dolinar and J. Marovt,Star partial order on B(H), Linear Algebra Appl. 434(1) (2011) 319–326. [3] K. Janich,Topology, Springer-Verlag, 1984. [4] J.L. Kelley, General Topology, Van Nostrand Company, Inc., Toronto-New York-London, 1955. [5] K. Menger,Probabilistic theories of relations, Proc. Nat. Acad. Sci. USA. 37 (1951) 178–180. [6] K. Menger,Probabilistic geometry, Proc. Nat. Acad. Sci. USA. 37 (1951) 226–229. [7] M. Mirzavaziri,Function valued metric space, Surv. Math. Appl. 5 (2010) 321–332. [8] M.S. Moslehian, On full Hilbert C*-modules, Bull. Malays. Math. Sci. Soc. 24 (2001) 45–47. [9] G.J. Murph,C ∗ -Algebras and Operator Theory, Academic Press, Inc., Boston, MA, 1990. [10] G.K. Pedersen, Analysis Now, Springer Verlag, 1988. [11] B. Schweizer and A. Sklar, Probabilistic metric space, North-Holland Series in Probability and Applied Mathematics. North-Holland Publishing Co., New York, (1983). | ||
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