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Bilinear module actions over quasi-ideals | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 30 تیر 1405 اصل مقاله (325.46 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2025.35426.5277 | ||
| نویسنده | ||
| Marjan Adib* | ||
| Department of Basic Sciences, Technical and Vocational University (TVU), Tehran, Iran | ||
| تاریخ دریافت: 03 مهر 1403، تاریخ بازنگری: 14 تیر 1404، تاریخ پذیرش: 08 مرداد 1404 | ||
| چکیده | ||
| 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 \( L_1(G)^* \). | ||
| کلیدواژهها | ||
| Factorable Banach algebra؛ Module action؛ Strict topology؛ quasi-ideal | ||
| مراجع | ||
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[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. | ||
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