References
-
J. P. Antoine, A. Inoue, and C. Trapani,
$O^\ast$ -dynamical systems and$\ast$ -derivations of unbounded operator algebras, Math. Nachr. 204 (1999), 5-28. https://doi.org/10.1002/mana.19992040102 -
J. P. Antoine, A. Inoue, and C. Trapani, Partial
$\ast$ -Algebras and Their Operator Realizations, Kluwer, Dordrecht, 2002. -
F. Bagarello, Applications of topological
$\ast$ -algebras of unbounded operators, J. Math. Phys. 39 (1998), no. 11, 6091-6105. https://doi.org/10.1063/1.532615 -
F. Bagarello, A. Inoue, and C. Trapani, Some classes of topological quasi
$\ast$ -algebras, Proc. Amer. Math. Soc. 129 (2001), no. 10, 2973-2980. https://doi.org/10.1090/S0002-9939-01-06019-1 -
F. Bagarello, A. Inoue, and C. Trapani, Derivations of quasi
$\ast$ -algebras, Int. J. Math. Math. Sci. 2004 (2004), no. 21-24, 1077-1096. https://doi.org/10.1155/S0161171204307155 -
F. Bagarello, A. Inoue, and C. Trapani, Exponentiating derivations of quasi
$\ast$ -algebras: possible approaches and applications, Int. J. Math. Math. Sci. 2005 (2005), no. 17, 2805-2820. https://doi.org/10.1155/IJMMS.2005.2805 -
F. Bagarello and C. Trapani, States and representations of
$CQ^\ast$ -algebras, Ann. Inst. H. Poincare Phys. Theor. 61 (1994), no. 1, 103-133. -
F. Bagarello and C. Trapani,
$CQ^\ast$ -algebras: structure properties, Publ. Res. Inst. Math. Sci. 32 (1996), no. 1, 85-116. https://doi.org/10.2977/prims/1195163181 - S. Czerwik, Functional Equations and Inequalities in Several Variables, World Scientific Publishing Company, New Jersey, London, Singapore and Hong Kong, 2002.
- S. Czerwik, Stability of Functional Equations of Ulam-Hyers-Rassias Type, Hadronic Press, Palm Harbor, Florida, 2003.
- Z. Gajda, On stability of additive mappings, Int. J. Math. Math. Sci. 14 (1991), no. 3, 431-434. https://doi.org/10.1155/S016117129100056X
- P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl. 184 (1994), no. 3, 431-436. https://doi.org/10.1006/jmaa.1994.1211
- D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A. 27 (1941), 222-224. https://doi.org/10.1073/pnas.27.4.222
- D. H. Hyers, G. Isac, and Th. M. Rassias, Stability of Functional Equations in Several Variables, Birkhauser, Basel, 1998.
- D. H. Hyers and Th. M. Rassias, Approximate homomorphisms, Aequationes Math. 44 (1992), no. 2-3, 125-153. https://doi.org/10.1007/BF01830975
-
C. Park, Lie
$\ast$ -homomorphisms between Lie$C^\ast$ -algebras and Lie$\ast$ -derivations on Lie$C^\ast$ -algebras, J. Math. Anal. Appl. 293 (2004), no. 2, 419-434. https://doi.org/10.1016/j.jmaa.2003.10.051 -
C. Park, Homomorphisms between Lie
$JC^\ast$ -algebras and Cauchy-Rassias stability of Lie$JC^\ast$ -algebra derivations, J. Lie Theory 15 (2005), no. 2, 393-414. -
C. Park, Isomorphisms between unital
$C^\ast$ -algebras, J. Math. Anal. Appl. 307 (2005), no. 2, 753-762. https://doi.org/10.1016/j.jmaa.2005.01.059 -
C. Park, Approximate homomorphisms on
$JB^\ast$ -triples, J. Math. Anal. Appl. 306 (2005), no. 1, 375-381. https://doi.org/10.1016/j.jmaa.2004.12.043 -
C. Park, Isomorphisms between
$C^\ast$ -ternary algebras, J. Math. Phys. 47 (2006), no. 10, 103512, 12 pp. https://doi.org/10.1063/1.2359576 -
C. Park, Hyers-Ulam-Rassias stability of a generalized Apollonius-Jensen type additive mapping and isomorphisms between
$C^\ast$ -algebras, Math. Nachr. 281 (2008), no. 3, 402-411. https://doi.org/10.1002/mana.200510611 - J. M. Rassias, On approximation of approximately linear mappings by linear mappings, J. Funct. Anal. 46 (1982), no. 1, 126-130. https://doi.org/10.1016/0022-1236(82)90048-9
- J. M. Rassias, On approximation of approximately linear mappings by linear mappings, Bull. Sci. Math. (2) 108 (1984), no. 4, 445-446.
- J. M. Rassias, Solution of a problem of Ulam, J. Approx. Theory 57 (1989), no. 3, 268-273. https://doi.org/10.1016/0021-9045(89)90041-5
- J. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), no. 2, 297-300. https://doi.org/10.1090/S0002-9939-1978-0507327-1
- J. M. Rassias, Problem 16; 2, Report of the 27th International Symp. on Functional Equations, Aequationes Math. 39 (1990), 292-293; 309.
- J. M. Rassias, The problem of S. M. Ulam for approximately multiplicative mappings, J. Math. Anal. Appl. 246 (2000), no. 2, 352-378. https://doi.org/10.1006/jmaa.2000.6788
- J. M. Rassias, On the stability of functional equations in Banach spaces, J. Math. Anal. Appl. 251 (2000), no. 1, 264-284. https://doi.org/10.1006/jmaa.2000.7046
- J. M. Rassias, On the stability of functional equations and a problem of Ulam, Acta Appl. Math. 62 (2000), no. 1, 23-130. https://doi.org/10.1023/A:1006499223572
- J. M. Rassias, Functional Equations, Inequalities and Applications, Kluwer Academic Publishers, Dordrecht, Boston and London, 2003.
- Th. M. Rassias and P. Semrl, On the Hyers-Ulam stability of linear mappings, J. Math. Anal. Appl. 173 (1993), no. 2, 325-338. https://doi.org/10.1006/jmaa.1993.1070
- F. Skof, Proprieta localie approssimazione di operatori, Rend. Sem. Mat. Fis. Milano 53 (1983), 113-129. https://doi.org/10.1007/BF02924890
-
C. Trapani, Quasi-
$\ast$ -algebras of operators and their applications, Rev. Math. Phys. 7 (1995), no. 8, 1303-1332. https://doi.org/10.1142/S0129055X95000475 -
C. Trapani, Some seminorms on quasi-
$\ast$ -algebras, Studia Math. 158 (2003), no. 2, 99-115. https://doi.org/10.4064/sm158-2-1 -
C. Trapani, Bounded elements and spectrum in Banach quasi
$\ast$ -algebras, Studia Math. 172 (2006), no. 3, 249-273. https://doi.org/10.4064/sm172-3-4 - S. M. Ulam, Problems in Modern Mathematics, Wiley, New York, 1960.
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