Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 17 (2022), 79 -- 88

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

APPROXIMATE θ-MULTIPLIERS ON BANACH ALGEBRAS

Abbas Zivari-Kazempour

Abstract. We show that each approximate θ-multiplier T: A ⟶ A on without order Banach algebra A is an exact θ-multiplier, and for every approximate θ-multiplier T there corresponds a unique θ-multiplier near to T. Moreover, each mapping S: A ⟶ A which is near to θ-multiplier T is approximate θ-multiplier. Some useful results about θ-multiplier of Banach algebras are given as well.

2020 Mathematics Subject Classification: 47A10; 46J10.
Keywords: (approximate) θ-multiplier; without order; almost homomorphism.

Full text

References

  1. E. Albas, On τ-centralizers of semiprime rings, Sib. Math. J., 48(2)(2007), 191-196. MR2330057. Zbl 1153.16028.

  2. H. G. Dales, Banach algebras and automatic continuity, London Mathematical Society, Monograph 24, Clarendon Press, Oxford, 2000. MR1816726. Zbl 0981.46043.

  3. Z. Gajda, On stability of additive mappings, Int. J. Math. Math. Sci., 14(3)(1991), 431-434. MR1110036. Zbl 0739.39013.

  4. D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U. S. A., 27(1941), 222-224. MR0004076. Zbl 0061.26403.

  5. S. Helgason, Multipliers of Banach algebras, Ann. Math., 64(1956), 240-254. MR0082075. Zbl 0072.32303.

  6. K. Jarosz, Perturbations of Banach algebras, Lecture Notes in Mathematics, Springer-Verlag, Berlin, 1985. MR0788884. Zbl 0557.46029.

  7. B. E. Johnson, An introduction to the theory of centralizers, Proc. London Math. Soc., 14(1964), 299-320. MR0159233. Zbl 0143.36102.

  8. B. E. Johnson, The uniqueness of the (complete) norm topology, Bull. Amer. Math. Soc., 73(1967), 537-539. MR0211260. Zbl 0172.41004.

  9. B. E. Johnson, Approximately multiplicative functionals, J. Lond. Math. Soc., 34(2)(1986), 489-510. MR0864452. Zbl 0625.46059.

  10. R. Larsen, An introduction to the theory of multipliers, Berlin, New York, Springer-Verlag, 1971. MR0435738. Zbl 0213.13301.

  11. T. Miura, G. Hirasawa, S-E. Takahasi, Stability on multipliers on Banach algebrs, Int. J. Math. Math. Sci., 45(2004), 2377-2381. https://doi.org/10.1155/S0161171204402324.

  12. I. Nikoufar and Th. M. Rassias, On θ-centralizers of semiprime Banach *-algebras, Ukrainian Math. J., 66(2)(2014), 300-310. Zbl 1351.46049.

  13. Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72(2)(1978), 297-300. MR0507327. Zbl 0398.47040.

  14. T. M. Rassias and P. Semrl, On the behavior of mappings which do not satisfy Hyers-Ulam stability, Proc. Amer. Math. Soc., 114(4)(1992), 989-993. MR337774. Zbl 0761.47004.

  15. P. Semrl, Almost multiplicative functions and almost linear multiplicative functionals, Aequationes Math., 63(2002), 189-192. MR1891286. Zbl 1007.39024.

  16. S. M. Ulam, Problems in Modern Mathematics, Chap. VI, Wiley, New York, 1964. MR3307658. Zbl 0137.24201.

  17. P. Wendel, Left Centralizers and isomorphisms on group algebras, Pacifi J. Math., 2(1952), 251-261. MR0049911. Zbl 0049.35702.

  18. A. Zivari-Kazempour, Almost multipliers of Frechet algebras, The J. Anal., 28(4)(2020), 1075-1084. MR4181916.



Abbas Zivari-Kazempour
Department of Mathematics, Ayatollah Borujerdi University, Borujerd, Iran.
e-mail: zivari@abru.ac.ir, zivari6526@gmail.com
http://abru.ac.ir

http://www.utgjiu.ro/math/sma