충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제24권2호
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  • Pages.221-238
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  • 2011
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  • 1226-3524(pISSN)
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  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
권호 표지
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LINEAR MAPPINGS IN BANACH MODULES OVER A UNITAL C*-ALGEBRA

  • 투고 : 2011.02.14
  • 심사 : 2011.05.18
  • 발행 : 2011.06.30
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초록

We prove the Hyers-Ulam stability of generalized Jensen's equations in Banach modules over a unital $C^{\ast}$-algebra. It is applied to show the stability of generalized Jensen's equations in a Hilbert module over a unital $C^{\ast}$-algebra. Moreover, we prove the stability of linear operators in a Hilbert module over a unital $C^{\ast}$-algebra.

키워드

과제정보

연구 과제 주관 기관 : National Research Foundation of Korea

참고문헌

  1. M. Albert and J. A. Baker, Bounded solutions of a functional inequality, Canad. Math. Bull. 25 (1982), 491-495. https://doi.org/10.4153/CMB-1982-071-9
  2. L. Baggett and A. Kleppner, Multiplier representations of abelian groups, J. Funct. Anal. 14 (1973), 299-324 https://doi.org/10.1016/0022-1236(73)90075-X
  3. J. A. Baker, On a theorem of Daroczy, Lajko and Szekelyhidi, Publ. Math. Debrecen 27 (1980), 283-288.
  4. J. A. Baker, The stability of the cosine equation, Proc. Amer. Math. Soc. 80 (1980), 411-416. https://doi.org/10.1090/S0002-9939-1980-0580995-3
  5. J. A. Baker and K. R. Davidson, Cosine exponential and quadratic functions, Glas. Mat. Ser. III 16 (1981), 269-274.
  6. J. A. Baker, J. Lawrence and F. Zorzitto, The stability of the equation f(x + y) = f(x)f(y), Proc. Amer. Math. Soc. 74 (1979), 242-246
  7. B. Blackadar, A. Kumjian and M. Rordam, Approximately central matrix units and the structure of noncommutative tori, K-Theory 6 (1992), 267-284. https://doi.org/10.1007/BF00961466
  8. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer-Verlag, New York, Heidelberg and Berlin, 1973.
  9. J. B. Conway, A Course in Functional Analysis, Springer-Verlag, New York, Berlin, Heidelberg and Tokyo, 1985.
  10. K. R. Davidson, $C^{\ast}$-Algebras by Example, Fields Institute Monographs, vol. 6, Amer. Math. Soc., Providence, R.I., 1996.
  11. D. H. Hyers, G. Isac and Th. M. Rassias, Stability of Functional Equations in Several Variables, Birkhauser, Berlin, Basel and Boston, 1998.
  12. R. Kadison and G. Pedersen, Means and convex combinations of unitary operators, Math. Scand. 57 (1985), 249-266. https://doi.org/10.7146/math.scand.a-12116
  13. P. S. Muhly and B. Solel, Hilbert modules over operator algebras, Memoirs Amer. Math. Soc. 117 (1995), no. 559, 1-53.
  14. Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300. https://doi.org/10.1090/S0002-9939-1978-0507327-1
  15. H. Schroder, K-Theory for Real $C^{\ast}$-Algebras and Applications, Pitman Research Notes in Mathematics, vol. 290, Longman, Essex, 1993.