Bilinear module actions over quasi-ideals

Articles in Press

Document Type : Research Paper

Author
Marjan Adib
Department of Basic Sciences, Technical and Vocational University (TVU), Tehran, Iran
10.22075/ijnaa.2025.35426.5277
Abstract
In this paper, we investigate certain properties and characterizations of bilinear module actions over quasi-ideals of a Banach algebra. Our results are applied to the quasi-ideals of the group algebra \( M(G) \), where we demonstrate that \( M(G) \) is isomorphic to a subspace of the space \( \mathcal{B}_{mod}(L_1(G)^*) \) consisting of all bilinear and separately continuous right module actions over \( L_1(G)^* \).
Keywords
Factorable Banach algebra
Module action
Strict topology
quasi-ideal
[1] M. Adib, Some topology on the space of quasi‑multipliers, Bull. Iran. Math. Soc. 5 (2017), 1323-1332.
[2] M. Adib and L.A. Khan, Strict topologies on topological algebras of quasi‑multipliers, Bull. Iran. Math. Soc. 48 (2022), 435-446.
[3] M. Adib, A. Riazi, and J. Bracic, Quasi‑multipliers of the dual of a Banach algebra, Banach J. Math. Anal. 5 (2011), 6-14.
[4] M. Adib, A. Riazi, and L.A. Khan, Quasi‑multipliers on F‑algebras, Abstr. Appl. Anal. 235273 (2011), 1-30.
[5] C.A. Akemann and G.K. Pedersen, Complications of semicontinuity in C∗‑algebra theory, Duke Math. J. 40 (1973), 785-795.
[6] Z. Argun and K. Rowlands, On quasi‑multipliers, Stud. Math. 108 (1994), no. 3, 217-245.
[7] M.S. Kassem and K. Rowlands, The quasi‑strict topology on the space of quasi‑multipliers of a B∗‑algebra, Math. Proc. Camb. Philos. Soc. 101 (1987), 555-566.
[8] L.A. Khan, The general strict topology on topological modules, Function spaces. Contemporary Mathematics, vol. 435 (2007), pp. 253-263, American Mathematical Society, Providence.
[9] L.A. Khan, Topological modules of continuous homomorphisms, J. Math. Anal. Appl. 343 (2008), 141-150.
[10] K. McKennon, Quasi‑multipliers, Trans. Amer. Math. Soc. 233 (1977), 105-123.
[11] M.A. Rieffel, Induced Banach representations of Banach algebras and locally compact groups, J. Funct. Anal. 1 (1967), 443-491.
[12] M.A. Rieffel, Multipliers and tensor products on Lp‑spaces of locally compact groups, Stud. Math. 33 (1969), 71-82.
[13] R. Yilmaz and K. Rowlands, On orthomorphisms, quasi‑orthomorphisms and quasi‑multipliers, J. Math. Anal. Appl. 313 (2006), 120-131.
International Journal of Nonlinear Analysis and Applications

Articles in Press, Corrected Proof
Available Online from 21 July 2026

  • Receive Date 24 September 2024
  • Revise Date 05 July 2025
  • Accept Date 30 July 2025