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Information Journal Paper

Title

𝛅-homomorphism maps into dual Banach algebras

Pages

  15-22

Abstract

 Let A be a Banach algebra and (B, B_*) be a dual Banach algebra. A linear map φ : A⟶ B is said to be a δ-homomorphism map if ‖ ‖ φ (a_1 a_2)-φ (a_1)φ (a_2)‖ ‖ ≤ δ ‖ ‖ a_1‖ ‖ ‖ ‖ a_2 ‖ ‖ for every a_1, a_2∈ A. In this paper, we study the δ-homomorphism maps from A into B. Among other things, we prove that if φ : A⟶ B is a δ-homomorphism map and B_* is multiplicative on the algebra generated by φ (A), then φ is bounded and ‖ ‖ φ ‖ ‖ ≤ 1+δ . Let A be a Banach algebra and (B, B_*) be a dual Banach algebra. A linear map φ : A⟶ B is said to be a δ-homomorphism map if ‖ ‖ φ (a_1 a_2)-φ (a_1)φ (a_2)‖ ‖ ≤ δ ‖ ‖ a_1‖ ‖ ‖ ‖ a_2 ‖ ‖ for every a_1, a_2∈ A. In this paper, we study the δ-homomorphism maps from A into B. Among other things, we prove that if φ : A⟶ B is a δ-homomorphism map and B_* is multiplicative on the algebra generated by φ (A), then φ is bounded and ‖ ‖ φ ‖ ‖ ≤ 1+δ .

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    APA: Copy

    HAYATI, B., & KHODAEI, H.. (2020). 𝛅-homomorphism maps into dual Banach algebras. JOURNAL OF NEW RESEARCHES IN MATHEMATICS, 5(21 ), 15-22. SID. https://sid.ir/paper/257246/en

    Vancouver: Copy

    HAYATI B., KHODAEI H.. 𝛅-homomorphism maps into dual Banach algebras. JOURNAL OF NEW RESEARCHES IN MATHEMATICS[Internet]. 2020;5(21 ):15-22. Available from: https://sid.ir/paper/257246/en

    IEEE: Copy

    B. HAYATI, and H. KHODAEI, “𝛅-homomorphism maps into dual Banach algebras,” JOURNAL OF NEW RESEARCHES IN MATHEMATICS, vol. 5, no. 21 , pp. 15–22, 2020, [Online]. Available: https://sid.ir/paper/257246/en

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