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Information Journal Paper

Title

Arens regularity of module actions

Pages

  141-148

Abstract

 Let A be a Banach algebra, A’ ’ a Banach A-module. In this paper, we give a simple criterion for the Arens regularity of a bilinear mapping on normed spaces, which applies in particular to Banach module actions, and them investigate those conditions under which the second adjoint of a derivation into a dual Banach algebra module is again a derivation. As a consequence of the main result, a simple and direct proof for several older results is also included. A^(4) is a Banach algebra with four Arens products. The bilinear map T is Arens regular when the equality T*** = T^( r***r ). If T: A × A’ ’ → A’ ’ is multiplication left module on A, the following statements are equivalent, i: T is regular ii: T**** = T^(r****r) iii: T****( A’ ’ ’ , A’ ’ ) ⊆ A’ ’ ’ iv: the linear map a → T*( a’ ’ ’ , a): A → A’ ’ ’ is weakly compact for every a’ ’ ’ ∈ A’ ’ ’ . Also If module actions are regular, then every inner derivation D: A → A’ ’ ’ is weakly compact; moreover, D**: (A’ ’ , □ ) → A^(5) and D**: (A’ ’ , ⋄ ) → A^(5) are also inner derivation.

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    APA: Copy

    SHABANI SOLTANMORADI, MEHRDAD, & Ebrahimi Bagha, Davood. (2020). Arens regularity of module actions. JOURNAL OF NEW RESEARCHES IN MATHEMATICS, 6(25 ), 141-148. SID. https://sid.ir/paper/954132/en

    Vancouver: Copy

    SHABANI SOLTANMORADI MEHRDAD, Ebrahimi Bagha Davood. Arens regularity of module actions. JOURNAL OF NEW RESEARCHES IN MATHEMATICS[Internet]. 2020;6(25 ):141-148. Available from: https://sid.ir/paper/954132/en

    IEEE: Copy

    MEHRDAD SHABANI SOLTANMORADI, and Davood Ebrahimi Bagha, “Arens regularity of module actions,” JOURNAL OF NEW RESEARCHES IN MATHEMATICS, vol. 6, no. 25 , pp. 141–148, 2020, [Online]. Available: https://sid.ir/paper/954132/en

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