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2004•Acta Scientiarum Naturalium Universitatis SunyatseniRequires access

Universal Jensen＇s Equations in Banach Modules over a C^＊-Algebra and Its Unitary Group

Chun-GilPark

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Abstract

In this paper, we prove the generalized Hyers-Ulam-Rassias stability of universal Jensen's equations in Banach modules over a unital C^*-algebra. It is applied to show the stability of universal Jensen's equations in a Hilbert module over a unital C^*-algebra. Moreover, we prove the stability of linear operators in a Hilbert module over a unital C^*-algebra.

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What this paper is about

In this paper, we prove the generalized Hyers-Ulam-Rassias stability of universal Jensen's equations in Banach modules over a unital C^*-algebra. It is applied to show the stability of universal Jensen's equations in a Hilbert module over a unital C^*-algebra. Moreover, we prove the stability of linear operators in a Hilbert module over a unital C^*-algebra.

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Available abstract

In this paper, we prove the generalized Hyers-Ulam-Rassias stability of universal Jensen's equations in Banach modules over a unital C^*-algebra. It is applied to show the stability of universal Jensen's equations in a Hilbert module over a unital C^*-algebra. Moreover, we prove the stability of linear operators in a Hilbert module over a unital C^*-algebra.

Key concepts: Mathematics, Unital, Banach algebra, Unitary state, Pure mathematics, Group (periodic table), Algebra over a field, Stability (learning theory)

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Universal Jensen＇s Equations in Banach Modules over a C^＊-Algebra and Its Unitary Group — Research Paper | ScholarLens