A SURVEY ON χ-MODULE CONNES AMENABILITY OF SEMIGROUP ALGEBRAS | ||
| Journal of Algebraic Systems | ||
| دوره 13، شماره 1، تیر 2025، صفحه 53-67 اصل مقاله (160.08 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2023.12900.1702 | ||
| نویسندگان | ||
| Ebrahim Tamimi* 1؛ Ali Ghaffari2 | ||
| 1Department of Mathematics, Velayat University, P.O. Box 9917638733, Iranshahr, Iran. | ||
| 2Department of Mathematics, University of Semnan, P.O. Box 35195-363, Semnan, Iran. | ||
| چکیده | ||
| We shall study the χ-module Connes amenability of a semigroup algebra l^1(S),where χ is a bounded module homomorphism from l^1(S) to l^1(S) that is w^∗-continuous and S is an inverse weakly cancellative semigroup with subsemigroup E of idempotents. We are mainly concerned with the study of χ-module normal, virtual diagonals. We characterize the χ- module Connes amenability of a semigroup algebra l^1(S). Also, we show that if l^1(S) as a Banach module over l^1(E) has an id-module normal, virtual diagonal then it is id-module Connes amenable. Other characterizations of χ- module Connes amenability of l^1(S) is presented. | ||
| کلیدواژهها | ||
| χ-module Connes amenable؛ module χ-derivation؛ χ-module normal virtual diagonal؛ weakly cancellative semigroup | ||
| مراجع | ||
|
1. M. Amini, Module amenability for semigroup algebras, Semigroup Forum, 69 (2004), 243–254.
2. M. Amini, A. Bodaghi and D. E. Bagha, Module amenability of the second dual and module topological center of semigroup algebras, Semigroup Forum, 80 (2010), 302–312.
3. M. Amini and R. Rezavand, Module operator virtual diagonals on the Fourier algebra of an inverse semigroup, Semigroup Forum, 97 (2018), 562–570.
4. H. G. Dales, A. T.-M. Lau and D. Strauss, Banach algebras on Semigroups and on their compactifications, American Mathematical Society, 2010.
5. H. G. Dales and D. Strauss, Arens regularity for totally ordered semigroups,Semigroup Forum, 105(1) (2022), 172–190.
6. M. Daws, Connes amenability of bidual and weighted semigroup algebras, Math. Scand., 99 (2006), 217–246.
7. A. Ghaffari and S. Javadi, φ-Connes amenability of dual Banach algebras, Bull. Iranian Math. Soc., 43 (2017), 25–39.
8. A. Ghaffari, S. Javadi and E. Tamimi, φ- module Connes amenability of dual Banach Algebras, J. Algebr. Syst., 8(1) (2020), 69–82.
9. B. E. Johnson, Cohomology in semigroup Algebras, Mem. Amer. Math. Soc., 127 (1972).
10. A. T.-M. Lau, Normal Structure and Common Fixed Point Properties for Semigroups of Nonexpansive Mappings in Banach Spaces, Fixed Point Theory and Applications, (2010), 1–14.
11. A. T.-M. Lau and Y. Zhang, Algebraic and analytic properties of semigroups related to fixed point properties of non-expansive mappings, Semigroup Forum, (2020), 1–26.
12. A. T.-M. Lau and Y. Zhang, Fixed point properties for semigroups of nonexpansive mappings on convex sets in dual Banach spaces, Ann. Univ. Paedagog. Crac. Stud. Math., 17 (2018), 67–87.
13. A. T.-M. Lau and Y. Zhang, Fixed point properties of semigroups of non-expansive mappings, J. Funct. Anal., 254 (2008), 2534–2554.
14. A. Minapoor, Ideal Connes amenability of l1-Munn algebras and its application to semigroup algebras,Semigroup Forum, 102(4) (2021), 756–764.
15. A. Minapoor, A. Bodagh and O. T. Mewomo, Ideal Connes-amenability of Lau product of Banach algebras, Eurasian Math. J., 12(4) (2021), 74–81.
16. W. D. Munn, A class of irreducible matrix representations of an arbitrary inverse semigroup, Proc. Glasgow Math. Assoc., 5 (1961), 41–48.
17. R. Rezavand, M. Amini, M. H. Sattari and D. E. Bagha, Module Arens regularity for semigroup algebras, Semigroup Forum, 77 (2008), 300–305.
18. W. Rudin, Functional Analysis, McGraw Hill, New York, 1991.
19. V. Runde, Amenability for dual Banach algebras, Studia Math., 148 (2001), 47–66.
20. V. Runde, Connes amenability and normal virtual diagonals for measure algebras I, J. London Math. Soc., 67 (2003), 643–656.
21. V. Runde, Lectures on Amenability, Springer New York, 2002 | ||
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