Proper \(CQ^*\)-ternary algebras
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2010
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Authors
Choonkil Park
- Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, Republic of Korea.
Abstract
In this paper, modifying the construction of a \(C^*\)-ternary algebra from a given \(C^*\)-algebra, we define a
proper \(CQ^*\)-ternary algebra from a given proper \(CQ^*\)-algebra.
We investigate homomorphisms in proper \(CQ^*\)-ternary algebras and derivations on proper \(CQ^*\)-ternary
algebras associated with the Cauchy functional inequality
\[\|f(x) + f(y) + f(z)\| \leq\| f(x + y + z)\|.\]
We moreover prove the Hyers-Ulam stability of homomorphisms in proper \(CQ^*\)-ternary algebras and of
derivations on proper \(CQ^*\)-ternary algebras associated with the Cauchy functional equation
\[f(x + y + z) = f(x) + f(y) + f(z).\]
Share and Cite
ISRP Style
Choonkil Park, Proper \(CQ^*\)-ternary algebras, Journal of Nonlinear Sciences and Applications, 7 (2014), no. 4, 278--287
AMA Style
Park Choonkil, Proper \(CQ^*\)-ternary algebras. J. Nonlinear Sci. Appl. (2014); 7(4):278--287
Chicago/Turabian Style
Park, Choonkil. "Proper \(CQ^*\)-ternary algebras." Journal of Nonlinear Sciences and Applications, 7, no. 4 (2014): 278--287
Keywords
- proper \(CQ^*\)-ternary homomorphism
- proper \(CQ^*\)-ternary derivation
- Cauchy functional equation
- Hyers-Ulam stability.
MSC
- 47B48
- 39B72
- 47J05
- 39B52
- 17A40
- 47L60
References
-
[1]
M. Adam, On the stability of some quadratic functional equation, J. Nonlinear Sci. Appl., 4 (2011), 50-59.
-
[2]
M. Amyari, M. S. Moslehian , Approximately ternary semigroup homomorphisms, Lett. Math. Phys., 77 (2006), 1-9.
-
[3]
J. P. Antoine, A. Inoue, C. Trapani, Partial *-Algebras and Their Operator Realizations, Kluwer, Dordrecht (2002)
-
[4]
F. Bagarello, Applications of topological *-algebras of unbounded operators, J. Math. Phys., 39 (1998), 6091-6105.
-
[5]
F. Bagarello , Fixed point results in topological *-algebras of unbounded operators, Publ. RIMS Kyoto Univ., 37 (2001), 397-418.
-
[6]
F. Bagarello, Applications of topological *-algebras of unbounded operators to modified quons, Nuovo Cimento B, 117 (2002), 593-611.
-
[7]
F. Bagarello, C. Trapani, A note on the algebraic approach to the ''almost'' mean field Heisenberg model, Nuovo Cimento B, 108 (1993), 779-784.
-
[8]
F. Bagarello, C. Trapani, States and representations of \(CQ^*\)-algebras, Ann. Inst. H. Poincaré, 61 (1994), 103-133.
-
[9]
F. Bagarello, C. Trapani, The Heisenberg dynamics of spin systems: a quasi-*-algebras approach, J. Math. Phys., 37 (1996), 4219-4234.
-
[10]
F. Bagarello, C. Trapani, S. Triolo, Quasi *-algebras of measurable operators, Studia Math., 172 (2006), 289-305.
-
[11]
L. Cădariu, L. Găvruţa, P. Găvruţa , On the stability of an affine functional equation, J. Nonlinear Sci. Appl., 6 (2013), 60-67.
-
[12]
A. Chahbi, N. Bounader, On the generalized stability of d'Alembert functional equation, J. Nonlinear Sci. Appl., 6 (2013), 198-204.
-
[13]
S. Czerwik , Functional Equations and Inequalities in Several Variables, World Scientific Publishing Company, New Jersey, London, Singapore and Hong Kong (2002)
-
[14]
S. Czerwik, Stability of Functional Equations of Ulam-Hyers-Rassias Type, Hadronic Press, Palm Harbor, Florida (2003)
-
[15]
G. Z. Eskandani, P. Găruta, Hyers-Ulam-Rassias stability of pexiderized Cauchy functional equation in 2- Banach spaces, J. Nonlinear Sci. Appl., 5 (2012), 459-465.
-
[16]
Z. Gajda, On stability of additive mappings, Internat. J. Math. Math. Sci., 14 (1991), 431-434.
-
[17]
P. Găvruta , A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl., 184 (1994), 431-436.
-
[18]
D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A., 27 (1941), 222-224.
-
[19]
D. H. Hyers, G. Isac, Th. M. Rassias , Stability of Functional Equations in Several Variables, Birkhäuser, Basel (1998)
-
[20]
D. H. Hyers, G. Isac, Th. M. Rassias, On the asymptoticity aspect of Hyers-Ulam stability of mappings, Proc. Amer. Math. Soc., 126 (1998), 425-430.
-
[21]
G. Isac, Th. M. Rassias, Stability of \(\psi\)-additive mappings : Applications to nonlinear analysis, Internat. J. Math. Math. Sci., 19 (1996), 219-228.
-
[22]
S. Jung, On the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl., 204 (1996), 221-226.
-
[23]
C. Park , Homomorphisms between Poisson \(JC^*\)-algebras, Bull. Braz. Math. Soc., 36 (2005), 79-97.
-
[24]
C. Park, Approximate homomorphisms on \(JB^*\)-triples, J. Math. Anal. Appl., 306 (2005), 375-381.
-
[25]
C. Park , Isomorphisms between \(C^*\)-ternary algebras, J. Math. Phys., 47, no. 10, 103512 (2006)
-
[26]
C. Park, Orthogonal stability of a cubic-quartic functional equation, J. Nonlinear Sci. Appl., 5 (2012), 28-36.
-
[27]
C. Park, M. Eshaghi Gordji, A. Najati , Generalized Hyers-Ulam stability of an AQCQ-functional equation in non-Archimedean Banach spaces , J. Nonlinear Sci. Appl., 3 (2010), 272-281.
-
[28]
C. Park, Th. M. Rassias, Homomorphisms in \(C^*\)-ternary algebras and \(JB^*\)-triples, J. Math. Anal. Appl., 337 (2008), 13-20.
-
[29]
C. Park, Th. M. Rassias, Homomorphisms and derivations in proper \(JCQ^*\)-triples, J. Math. Anal. Appl., 337 (2008), 1404-1414.
-
[30]
J. M. Rassias, On approximation of approximately linear mappings by linear mappings, Bull. Sci. Math., 108 (1984), 445-446.
-
[31]
J. M. Rassias, Solution of a problem of Ulam, J. Approx. Theory, 57 (1989), 268-273.
-
[32]
M. J. Rassias, J. M. Rassias , product-sum stability of an Euler-Lagrange functional equation, J. Nonlinear Sci. Appl., 3 (2010), 265-271.
-
[33]
Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72 (1978), 297-300.
-
[34]
Th. M. Rassias, Problem 16, 2, Report of the 27th International Symp. on Functional Equations, Aequationes Math., 39 (1990), 292-293.
-
[35]
Th. M. Rassias, The problem of S.M. Ulam for approximately multiplicative mappings, J. Math. Anal. Appl., 246 (2000), 352-378.
-
[36]
Th. M. Rassias, On the stability of functional equations in Banach spaces , J. Math. Anal. Appl., 251 (2000), 264-284.
-
[37]
Th. M. Rassias, Functional Equations, Inequalities and Applications, Kluwer Academic Publishers, Dordrecht , Boston and London (2003)
-
[38]
Th. M. Rassias, P. Šemrl, On the behaviour of mappings which do not satisfy Hyers-Ulam stability , Proc. Amer. Math. Soc., 114 (1992), 989-993.
-
[39]
Th. M. Rassias, P. Šemrl , On the Hyers-Ulam stability of linear mappings, J. Math. Anal. Appl., 173 (1993), 325-338.
-
[40]
K. Ravi, E. Thandapani, B. V. Senthil Kumar , Solution and stability of a reciprocal type functional equation in several variables, J. Nonlinear Sci. Appl., 7 (2014), 18-27.
-
[41]
S. Schin, D. Ki, J. Chang, M. Kim, Random stability of quadratic functional equations: a fixed point approach , J. Nonlinear Sci. Appl., 4 (2011), 37-49.
-
[42]
F. Skof , Proprieta locali e approssimazione di operatori , Rend. Sem. Mat. Fis. Milano, 53 (1983), 113-129.
-
[43]
C. Trapani, Some seminorms on quasi-*-algebras, Studia Math., 158 (2003), 99-115.
-
[44]
C. Trapani , Bounded elements and spectrum in Banach quasi *-algebras, Studia Math., 172 (2006), 249-273.
-
[45]
S. M. Ulam , A Collection of the Mathematical Problems, Interscience Publ., New York (1960)
-
[46]
C. Zaharia , On the probabilistic stability of the monomial functional equation, J. Nonlinear Sci. Appl., 6 (2013), 51-59.
-
[47]
S. Zolfaghari, Approximation of mixed type functional equations in p-Banach spaces, J. Nonlinear Sci. Appl., 3 (2010), 110-122.
-
[48]
H. Zettl, A characterization of ternary rings of operators, Adv. Math., 48 (1983), 117-143.