A Non-Commutative Symmetric Algebra via Ş-Proximit Structure
Abstract
These axioms easily characterize the Gelfand theory of a commutative symmetric algebra. Numerous characteristics of commutative Gelfand theory are also presented in Gelfand theories of arbitrary symmetric algebras. We proved that symmetric algebras that are homogeneous and unital always have a Gelfand theory. We demonstrated that the identity is the unique Gelfand theory for liminal symmetric algebras with discrete spectrum (subject to a suitable concept of equivalence).
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References
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R. Lowen and S. Verwulgen, Approach vector spaces. Houston J. Math., 30(4) (2004) pp. 1127-1142.
W. Li and D.Zhang, sober metric approach spaces, Topol.Appl., 233 (2018)pp. 67-88.
R. Kadison and J. Ringrose, Fundamentals of the theory of operator algebras Elementary theory, (Academic Press, Inc., London, 1983).
Abed Ali S. and B. Hussein, “ New Kind of vector space via s-proximit structure, E3S web of conferences ,” (2024) pp.1-12.
B. Y. Hussein and H. A. A.washaych, “New Result of Q-Bounded fun dined in symmetric ∆- symmetric algebra ,AIP conference Processing (2023) pp. 1-7.
B.Y. Hussein and H. A.A. Wshyayeh, “On State Space of Measurable Function in Symmetric E- symmetric algebra with New Result,” AIP Conference Preceding (2022) pp. 1-7.
B.Y. Hussein and H. A.A. Wshyayeh, On State Space of Measurable Function in Symmetric ∆- symmetric algebra with New Results, Aip Conference Proceedings, 2022, 2398, 060064
B.Y. Hussein and S. S. Abd, On New Results of Normed Approach Space Via β- Approach structure. Iraqi journal of science, 64(7) (2022) pp. 3538-3550.
B.Y Hussein, Equivalent locally Martingale Measure for the deflator process on ordered symmetric algebra. Journal in Mathematics, 2020 (2020) pp. 1-7.
D. A. Kadhim, B.Y. Hussein, New Kind of topological vector space Via proximit structure. Journal of interdisciplinary Mathematics, 26(6) (2023) pp1065-1075.
D. A. Kadhim, B.Y. Hussein, A new type of metric space via proximit structure, Journal of Interdisciplinary Mathematics, 2023, 26(6), pp. 1053–1064.
F.F. Bosall and J. Duncan, Complete Normed Algebras. Springer Verlag, 1973.
G. Jameson, Topology and normed spaces, (Chapman and Hall, London,.Cambridge University Press, 2009).
Hussein, B.Y., Kream, A.A., A New Structure of Random approach Vector Space, Boletim Da Sociedade Paranaense De Matematica, 2025, 43.
Hussein, B.Y., Fahim, S., , Characterization on Fuzzy Soft Ordered symmetric algebra, Boletim Da Sociedade Paranaense De Matematica, 2022, 40.
I. Kaplansky, “Algebraic and analytic aspects of operator algebras,” Reg. Conf. Ser. Math., (1970) .
J. K. Wang, Multipliers of commutative symmetric algebra, Pacific J. Math. 11(1961),1131-1149.
R. Fleming and J. Jamison, Hermitian operators on C(X,E) and the -
Stone theorem, Math. Z. 170(3) (1980), pp.77- 84.
M. A. Neamah and B.Y. Hussein, Some New Result of Completion t^w Normed Approach space, Periodicals of Engineering and natural Sciences. 10(5)(2022) pp.82-89.
M. A. Neamah and B.Y. Hussein, New Result of t^w Normed Approach space. Journal of Interdisci plinary Mathematics, 26(6)(2023) pp. 1109-1121.
Neamah, M.A., Hussein, B.Y., On δ- character in symmetric tω-Δ- -algebra, Journal of Discrete Mathematical Sciences and Cryptography, 2023, 26(7), pp. 1939–1947.
Neamah, M.A., Hussein, B.Y. , On δ- character in symmetric tω-Δ- -algebra, Journal of Discrete Mathematical Sciences and Cryptography, 2023, 26(7), pp. 1939–1947
R. Abbas and B. Y. Hussein, “A New Kind of topological vector space:Topological approach vector space,” AIP Conference Preceding (2022) pp. 1-9.
R. K. Abbas and B. Y. Hussein, “New Result of completion Normed Approach Space,” AIP Conference Procceding. (2021).
R. K. Abbas and B. Y. Hussein, New Result of Normed Approach Space. Iraqi Journal of Science, 36(5) (2022) pp.2103-2113.
R. Baekeland and R. Lowen, Measures of Lindelof and separability in approach spaces. Int. J. Math. & Math. Sci., 17(3) (1994) pp.597-606.
R. Lowen , Approach space The missing link in the topology - uniformity-matric triad. (Oxford University press, 1997).
R. Lowen, M. Sioen, and D. Vaughan, Completing quasi-metric spaces| an alternative approach. Houston J. Math., 29(1) (2003) pp. 105-112.
R. Lowen and C. Verbeeck, Local compactness in approach spaces. I, Internat. J. Math. & Math. Sci., 21(3) (1998) pp. 429-438.
R. Lowen and F. Verbeeck, Local compactness in approach spaces: part II, Internat. J. Math. & Math. Sci., vol(2)(2003) pp. 109-117.
R. Lowen and S. Verwulgen, Approach vector spaces. Houston J. Math., 30(4) (2004) pp. 1127-1142.
W. Li and D.Zhang, sober metric approach spaces, Topol.Appl., 233 (2018)pp. 67-88.
R. Kadison and J. Ringrose, Fundamentals of the theory of operator algebras Elementary theory, (Academic Press, Inc., London, 1983).
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2025-09-30
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