• Title/Summary/Keyword: Banach module over Banach algebra

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LINEAR MAPPINGS IN BANACH MODULES OVER A UNITAL C*-ALGEBRA

  • Lee, Jung Rye;Mo, Kap-Jong;Park, Choonkil
    • Journal of the Chungcheong Mathematical Society
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    • v.24 no.2
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    • pp.221-238
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    • 2011
  • 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.

FUNCTIONAL EQUATIONS IN BANACH MODULES AND APPROXIMATE ALGEBRA HOMOMORPHISMS IN BANACH ALGEBRAS

  • Boo, Deok-Hoon;Kenary, Hassan Azadi;Park, Choonkil
    • Korean Journal of Mathematics
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    • v.19 no.1
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    • pp.33-52
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    • 2011
  • We prove the Hyers-Ulam stability of partitioned functional equations in Banach modules over a unital $C^*$-algebra. It is applied to show the stability of algebra homomorphisms in Banach algebras associated with partitioned functional equations in Banach algebras.

CYCLIC FUNCTIONAL EQUATIONS IN BANACH MODULES OVER A UNITAL $C^{*}$-ALGEBRA

  • Park, Chun-Gil
    • Journal of applied mathematics & informatics
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    • v.15 no.1_2
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    • pp.343-361
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    • 2004
  • We prove the generalized Hyers-Ulam-Rassias stability of cyclic functional equations in Banach modules over a unital $C^{*}$-algebra. It is applied to show the stability of algebra homomorphisms between Banach algebras associated with cyclic functional equations in Banach algebras.

GENERALIZED JENSEN'S FUNCTIONAL EQUATIONS AND APPROXIMATE ALGEBRA HOMOMORPHISMS

  • Bae, Jae-Hyeong;Park, Won-Gil
    • Bulletin of the Korean Mathematical Society
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    • v.39 no.3
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    • pp.401-410
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    • 2002
  • We prove the generalized Hyers-Ulam-Rassias stability of generalized Jensen's functional equations in Banach modules over a unital $C^{*}$-algebra. It is applied to show the stability of algebra homomorphisms between Banach algebras associated with generalized Jensen's functional equations in Banach algebras.