Browse > Article
http://dx.doi.org/10.4134/BKMS.2008.45.1.111

ISOMORPHISMS IN QUASI-BANACH ALGEBRAS  

Park, Choon-Kil (DEPARTMENT OF MATHEMATICS HANYANG UNIVERSITY)
An, Jong-Su (DEPARTMENT OF MATHEMATICS EDUCATION PUSAN NATIONAL UNIVERSITY)
Publication Information
Bulletin of the Korean Mathematical Society / v.45, no.1, 2008 , pp. 111-118 More about this Journal
Abstract
Using the Hyers-Ulam-Rassias stability method, we investigate isomorphisms in quasi-Banach algebras and derivations on quasi-Banach algebras associated with the Cauchy-Jensen functional equation $$2f(\frac{x+y}{2}+z)$$=f(x)+f(y)+2f(z), which was introduced and investigated in [2, 17]. The concept of Hyers-Ulam-Rassias stability originated from the Th. M. Rassias' stability theorem that appeared in the paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300. Furthermore, isometries and isometric isomorphisms in quasi-Banach algebras are studied.
Keywords
Cauchy-Jensen functional equation; isomorphism; isometry; derivation; quasi-Banach algebra;
Citations & Related Records

Times Cited By Web Of Science : 2  (Related Records In Web of Science)
Times Cited By SCOPUS : 4
연도 인용수 순위
1 C. Park, Homomorphisms between Poisson JC*-algebras, Bull. Braz. Math. Soc. (N.S.) 36 (2005), no. 1, 79-97   DOI
2 C. Park, A generalized Jensen's mapping and linear mappings between Banach modules, Bull. Braz. Math. Soc. (N.S.) 36 (2005), no. 3, 333-362   DOI
3 C. Park, Isomorphisms between C*-ternary algebras, J. Math. Phys. 47, no. 10, Article ID 103512 (2006), 12 pages
4 Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), no. 2, 297-300   DOI   ScienceOn
5 Th. M. Rassias, Problem 16; 2, Report of the 27th Internat. Symp. on Functional Equations, Aequationes Math. 39 (1990), 292-293; 309
6 Th. M. Rassias, Properties of isometic mappings, J. Math. Anal. Appl. 235 (1997), 108-121   DOI   ScienceOn
7 Th. M. Rassias, The problem of S. M. Ulam for approximately multiplicative mappings, J. Math. Anal. Appl. 246 (2000), no. 2, 352-378   DOI   ScienceOn
8 A. Gilanyi, Eine zur Parallelogrammgleichung aquivalente Ungleichung, Aequationes Math. 62 (2001), no. 3, 303-309   DOI
9 A. Gilanyi, On a problem by K. Nikodem, Math. Inequal. Appl. 5 (2002), no. 4, 707-710
10 D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U. S. A. 27 (1941), 222-224   DOI   ScienceOn
11 S. M. Ulam, Problems in Modern Mathematics, Science Editions John Wiley & Sons, Inc., New York, 1964
12 N. Kalton, An elementary example of a Banach space not isomorphic to its complex conjugate, Canad. Math. Bull. 38 (1995), no. 2, 218-222   DOI
13 Th. M. Rassias, On the stability of functional equations and a problem of Ulam, Acta Appl. Math. 62 (2000), no. 1, 23-130   DOI
14 Th. M. Rassias, Functional Equations, Inequalities and Applications, Kluwer Academic Publishers, Dordrecht, 2003
15 Th. M. Rassias and P. Semrl, On the Mazur-Ulam theorem and the Aleksandrov problem for unit distance preserving mappings, Proc. Amer. Math. Soc. 118 (1993), no. 3, 919-925   DOI   ScienceOn
16 W. Fechner, Stability of a functional inequality associated with the Jordan-von Neumann functional equation, Aequationes Math. 71 (2006), no. 1-2, 149-161   DOI
17 C. Park, Y. Cho, and M. Han, Functional inequalities associated with Jordan-von Neumann type additive functional equations, J. Inequal. Appl. 2007, Article ID 41820 (2007), 13 pages   DOI
18 Th. M. Rassias, On the stability of functional equations in Banach spaces, J. Math. Anal. Appl. 251 (2000), no. 1, 264-284   DOI   ScienceOn
19 J. Ratz, On inequalities associated with the Jordan-von Neumann functional equation, Aequationes Math. 66 (2003), no. 1-2, 191-200   DOI
20 S. Rolewicz, Metric Linear Spaces, Second edition. PWN-Polish Scientific Publishers, Warsaw; D. Reidel Publishing Co., Dordrecht, 1984
21 Y. Benyamini and J. Lindenstrauss, Geometric Nonlinear Functional Analysis. Vol. 1, American Mathematical Society Colloquium Publications, 48. American Mathematical Society, Providence, RI, 2000
22 M. Mirzavaziri and M. S. Moslehian, A fixed point approach to stability of a quadratic equation, Bull. Braz. Math. Soc. (N.S.) 37 (2006), no. 3, 361-376   DOI
23 J. M. Almira and U. Luther, Inverse closedness of approximation algebras, J. Math. Anal. Appl. 314 (2006), no. 1, 30-44   DOI   ScienceOn
24 C. Baak, Cauchy-Rassias stability of Cauchy-Jensen additive mappings in Banach spaces, Acta Math. Sin. (Engl. Ser.) 22 (2006), no. 6, 1789-1796   DOI
25 C. Baak and M. S. Moslehian, On the stability of ${\theta}$-derivations on JB*-triples, Bull. Braz. Math. Soc. (N.S.) 38 (2007), no. 1, 115-127   DOI
26 J. Baker, Isometries in normed spaces, Amer. Math. Monthly 78 (1971), 655-658   DOI   ScienceOn
27 J. Bourgain, Real isomorphic complex Banach spaces need not be complex isomorphic, Proc. Amer. Math. Soc. 96 (1986), no. 2, 221-226   DOI   ScienceOn
28 S. Mazur and S. Ulam, Sur les transformation d'espaces vectoriels norme, C. R. Acad. Sci. Paris 194 (1932), 946-948
29 C. Park, On an approximate automorphism on a C*-algebra, Proc. Amer. Math. Soc. 132 (2004), no. 6, 1739-1745   DOI   ScienceOn