An analytical innovation of Hilbert algebra via δ-approach structure

  • Boushra Y. Hussein Al-Qadisiyah university
  • Ayad J. M. Al-shebly

Abstract

This paper presents novel results within the framework of the multicharacter approach to Hilbert algebras, focusing on a refined analysis of multipliers and their algebraic behavior. The investigation systematically explores the interplay between fixed sets and their structural roles in shaping the internal dynamics of Hilbert algebras. Emphasis is placed on establishing rigorous connections through formal theorems and illustrative examples that clarify the utility and implications of the multicharacter perspective. By extending classical insights, the study provides a broader and more nuanced understanding of how multipliers operate within and influence the overall architecture of Hilbert algebras.

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References

R. Abbas. A New Structure of Banach Approach Space. M.sc. thesis, University of Al-Qadisiyah, 2021.

R.K. Abbas and Boushra Y. Hussein. New results of normed approach space. Iraqi Journal of Science, 63(5):2103–2113, 2022.

R.K. Abbas and B.Y. Hussein. A new kind of topological vector space: Topological approach vector space. AIP Conference Proceedings, 2386(1):060008, 2022.

R.K. Abbas and B.Y. Hussein. New results of normed approach space. Iraqi Journal of science, 63(5):2103–2113, 2022.

S.S.A. Ali and B.Y. Hussein. New kind of vector space via ş-proximit structure. E3S Web of Conferences, 508:04012, 2024.

R. Baekeland and R. Lowen. Measures of lindelof and separability in approach spaces. International Journal of Mathematics and Mathematical Sciences, 17(3):597–606, 1994.

R.J. Fleming and J.E. Jamison. Hermitian operators on c (x, e) and the banach-stone theorem. Mathematische Zeitschrift, 170:77–84, 1980.

Boushra Y. Hussein and Hadeer A. Wshayeh. New results of q-bounded functional in symmetric δ-banach algebra. AIP Conference Proceedings, 2845(1):050040, 2023.

B.Y. Hussein. Equivalent locally martingale measure for the deflator process on ordered banach algebra. Journal of Mathematics, 2020(1):5785098, 2020.

B.Y Hussein and R.K. Abbas. New results of completion normed approach space. AIP Conference Proceedings, 2845(1):050036, 2023.

B.Y. Hussein and Huda A.A. Wshayeh. On state space of measurable function in symmetric δ-banach algebra with new results. AIP Conference Proceedings, 2398(1):060064, 2022.

G. J. O. Jameson. Topology and Normed Spaces. Chapman and Hall, London, 1974.

D.A. Kadhim and B.Y. Hussein. New kind of topological vector space via proximity structure. Journal of Interdisciplinary Mathematics, 26(6):1065–1075, 2023.

R.V. Kadison and John R. Ringrose. Fundamentals of the Theory of Operator Algebras: Elementary Theory. Academic Press, Inc., London, 1983.

H. Kamowitz and S. Scheinberg. Some properties of endomorphisms of lipschitz algebras. Studia Mathematica, 96:255–261, 1990.

I. Kaplansky. Algebraic and Analytic Aspects of Operator Algebras. American Mathematical Society, Providence, RI, USA, 1970.

I. Kaplansky. Fields and Rings. The University of Chicago Press, Chicago, IL, USA, 2nd edition, 1972.

C. Kellogg. Centralizers and h∗-algebras. Pacific Journal of Mathematics, 17(1):121–129, 1966.

A.A. Kream and B.Y. Hussein. A new structure of random approach normed space via banach space. Iraqi Journal of Science, 65(10):5617–5628, 2024.

W. Li and D. Zhang. Sober metric approach spaces. Topology and its Applications, 233:67–88, 2018.

R. Lowen. Approach spaces a common supercategory of top and met. Mathematische Nachrichten, 141(1):183–226, 1989.

R. Lowen. Approach Spaces: The Missing Link in the Topology—Uniformity—Metric Triad. Oxford Mathematical Monographs. Oxford University Press, Oxford, 1997.

R. Lowen, D. Vaughan, and M. Sioen. Completing quasi metric spaces: An alternative approach. Houston Journal of Mathematics, 29(1):113–136, 2003.

R. Lowen and C. Verbeeck. Local compactness in approach spaces i. International Journal of Mathematics and Mathematical Sciences, 21(3):429–438, 1998.

R. Lowen and C. Verbeeck. Local compactness in approach spaces ii. International Journal of Mathematics and Mathematical Sciences, 2003(2):109–117, 2003.

R. Lowen and S. Verwulgen. Approach vector spaces. Houston Journal of Mathematics, 30(4):1127–1142, 2004.

M.A. Neamah and B.Y. Hussein. New result of tw normed approach space. Journal of Interdisciplinary Mathematics, 26(6):1109–1211, 2023.

Maysoon A Neamah and Boushra Y Hussein. Some new results of completion tω-normed approach space. Periodicals of Engineering and Natural Sciences (PEN), 10(5):82–89, 2022.

W. Rudin. Functional Analysis. McGraw-Hill, New York, 1991.

J.K. Wang. Multipliers of commutative banach algebra. Pacific Journal of Mathematics, 11:1131–1149, 1961.

Published
2025-07-12
Section
Research Articles