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On the stability of $$J^*$$-homomorphisms. (English) Zbl 1085.39026
The puspose of this paper is to prove the generalized Hyers-Ulam-Rassias stability of $$J^*$$-homomorphism between $$J^*$$-algebras. The reader is referred to the book of D. H. Hyers, G. Isac and Th. M. Rassias [Stability of functional equations in several variables (Birkhäuser, Boston, Basel, Berlin) (1998; Zbl 0907.39025)] for an extensive presentation of classical results and research problems on stability of mappings and their various applications. The result, that has been proved in the present paper, is particularly interesting and is expected to find applications to other problems in mathematical analysis.

##### MSC:
 39B82 Stability, separation, extension, and related topics for functional equations 39B52 Functional equations for functions with more general domains and/or ranges 46L05 General theory of $$C^*$$-algebras
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##### References:
 [1] Czerwik, S., Stability of functional equations of ulam – hyers – rassias type, (2003), Hadronic Press Nonantum, MA [2] Gajda, Z., On stability of additive mappings, Internat. J. math. math. sci., 14, 431-434, (1991) · Zbl 0739.39013 [3] Găvruta, P., A generalization of the hyers – ulam – rassias stability of approximately additive mappings, J. math. anal. appl., 184, 431-436, (1994) · Zbl 0818.46043 [4] L.A. Harris, Bounded symmetric homogeneous domains in infinite-dimensional spaces, Lecture Notes in Mathematics, vol. 364, Springer, Berlin, 1974. · Zbl 0293.46049 [5] Harris, L.A., Operator Siegel domains, Proc. roy. soc. Edinburgh sect. A., 79, 137-156, (1977) · Zbl 0376.32027 [6] Harris, L.A., A generalization of $$C^*$$-algebras, Proc. London math. soc., 42, 331-361, (1981) · Zbl 0476.46054 [7] Hyers, D.H., On the stability of the linear functional equation, Proc. natl. acad. sci. USA, 27, 222-224, (1941) · Zbl 0061.26403 [8] Kadison, R.V.; Pedersen, G.K., Means and convex combinations of unitary operators, Math. scand., 57, 249-266, (1985) · Zbl 0573.46034 [9] Park, C., On an approximate automorphism on a $$C^*$$-algebra, Proc. amer. math. soc., 132, 1739-1745, (2004) · Zbl 1055.47032 [10] Park, C., Lie $$*$$-homomorphisms between Lie $$C^*$$-algebras and Lie $$*$$-derivations on Lie $$C^*$$-algebras, J. math. anal. appl., 293, 419-434, (2004) · Zbl 1051.46052 [11] Rassias, Th.M., On the stability of the linear mapping in Banach spaces, Proc. amer. math. soc., 72, 297-300, (1978) · Zbl 0398.47040 [12] Rassias, Th.M.; Šemrl, P., On the behavior of mappings which do not satisfy hyers – ulam stability, Proc. amer. math. soc., 114, 989-993, (1992) · Zbl 0761.47004 [13] Ulam, S.M., Problems in modern mathematics, (1964), science ed. Wiley, New York, (Chapter VI) · Zbl 0137.24201
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