Poisson Banach Modules over a Poisson C*-Algebr

• Journal title : Kyungpook mathematical journal
• Volume 48, Issue 4,  2008, pp.529-543
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2008.48.4.529
Title & Authors
Poisson Banach Modules over a Poisson C*-Algebr
Park, Choon-Kil;

Abstract
It is shown that every almost linear mapping h : $\small{A{\rightarrow}B}$ of a unital PoissonC*-algebra A to a unital Poisson C*-algebra B is a Poisson C*-algebra homomorph when $h(2^nuy)\; Keywords Poisson C*-algebra homomorphism;Poisson Banach module;Poisson C*-algebra;stability;linear functional equation; Language English Cited by References 1. V. A. Faiziev, Th. M. Rassias and P. K. Sahoo, The space of$({\psi},{\gamma})-additive$mappings on semigroups, Trans. Amer. Math. Soc., 354(2002), 4455-4472. 2. P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl., bf 184(1994), 431-436. 3. K. R. Goodearl and E. S. Letzter, Quantum n-space as a quotient of classical n-space, Trans. Amer. Math. Soc., 352(2000), 5855-5876. 4. K. Jun and Y. Lee, A generalization of the Hyers-Ulam-Rassias stability of Jensen's equation, J. Math. Anal. Appl., 238(1999), 305-315. 5. R. V. Kadison and G. Pedersen, Means and convex combinations of unitary operators, Math. Scand., 57(1985), 249-266. 6. R. V. Kadison and J.R. Ringrose, Fundamentals of the Theory of Operator Algebras, Elementary Theory, Academic Press, New York, 1983. 7. S. Oh, C. Park and Y. Shin, Quantum n-space and Poisson n-space, Comm. Algebra, 30(2002), 4197-4209. 8. S. Oh, C. Park and Y. Shin, A Poincare-Birkhoff-Witt theorem for Poisson enveloping algebras, Comm. Algebra, 30(2002), 4867-4887. 9. C. Park, On the stability of the linear mapping in Banach modules, J. Math. Anal. Appl., 275(2002), 711-720. 10. C. Park, Modified Trif's functional equations in Banach modules over a$C^{\ast}-algebra\$ and approximate algebra homomorphisms, J. Math. Anal. Appl., 278(2003), 93-108.

11.
C. Park and W. Park, On the Jensen's equation in Banach modules, Taiwanese J. Math., 6(2002), 523-531.

12.
Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72(1978), 297-300.

13.
Th. M. Rassias, On the stability of functional equations and a problem of Ulam, Acta Appl. Math., 62(2000), 23-130.

14.
Th. M. Rassias, The problem of S.M. Ulam for approximately multiplicative mappings, J. Math. Anal. Appl., 246(2000), 352-378.

15.
Th. M. Rassias, On the stability of functional equations in Banach spaces, J. Math. Anal. Appl., 251(2000), 264-284.

16.
Th. M. Rassias and P. Semrl, On the behavior of mappings which do not satisfy Hyers-Ulam stability, Proc. Amer. Math. Soc., 114(1992), 989-993.

17.
Th. M. Rassias and P. Semrl, On the Hyers-Ulam stability of linear mappings, J. Math. Anal. Appl., 173(1993), 325-338.

18.
T. Trif, On the stability of a functional equation deriving from an inequality of Popoviciu for convex functions, J. Math. Anal. Appl., 272(2002), 604-616.

19.
P. Xu, Noncommutative Poisson algebras, Amer. J. Math., 116(1994), 101-125.