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On left $\phi$-Connes biprojectivity of dual Banach algebras | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 19، دوره 14، شماره 6، شهریور 2023، صفحه 257-264 اصل مقاله (412.22 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.23598.2563 | ||
| نویسندگان | ||
| Amir Sahami* 1؛ Eghbal Ghaderi2؛ S. Fatemeh Shariati3؛ Sayed Mehdi Kazemi Torbaghan4 | ||
| 1Department of Mathematics, Faculty of Basic Sciences, Ilam University, P.O. Box 69315-516, Ilam, Iran | ||
| 2Department of Mathematics, University of Kurdistan, Pasdaran Boulevard, Sanandaj 66177--15175, P. O. Box 416, Iran | ||
| 3Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Iran | ||
| 4Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, Bojnord, P.O.Box 94531, Iran | ||
| تاریخ دریافت: 14 خرداد 1400، تاریخ بازنگری: 14 شهریور 1400، تاریخ پذیرش: 16 مهر 1400 | ||
| چکیده | ||
| We introduce the notion of left (right) $\phi$-Connes biprojective for a dual Banach algebra $\mathcal{A}$, where $\phi$ is a non-zero $wk^*$-continuous multiplicative linear functional on $\mathcal{A}$. We discuss the relationship of left $\phi$-Connes biprojectivity with $\phi$-Connes amenability and Connes biprojectivity. For a unital weakly cancellative semigroup $S$, we show that $\ell^1(S)$ is left $\phi_{S}$-Connes biprojective if and only if $S$ is a finite group, where $\phi_{S}\in\Delta_{w^*}(\ell^1(S))$. We prove that for a non-empty totally ordered set $I$ with the smallest element, the upper triangular $I\times I$-matrix algebra $UP(I,\mathcal{A})$ is right $\psi_\phi$-Connes biprojective if and only if $\mathcal{A}$ is right $\phi$-Connes biprojective and $I$ is a singleton, provided that $\mathcal{A}$ has a right identity and $\phi\in\Delta_{w^*}(\mathcal{A})$. Also for a finite set $I$, if $Z({\mathcal A})\cap ({\mathcal A}-\ker\phi)\neq \emptyset$, then the dual Banach algebra $UP(I, {\mathcal A})$ under this new notion forced to have a singleton index | ||
| کلیدواژه‌ها | ||
| Semigroup algebras؛ Matrix algebras؛ Connes amenability؛ Left $\phi$-Connes biprojectivity | ||
| مراجع | ||
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[1] H.G. Dales, A.T.M. Lau and D. Strauss, Banach algebras on semigroups and their compactifications, Memoir Amer. Math. Soc. 966 (2010). [2] A. Ghaffari and S. Javadi, ϕ-Connes amenability of dual Banach algebras, Bull. Iran. Math. Soc. 43 (2017), no.1, 25–39. [3] A.Ya. Helemskii, The homology of Banach and topological algebras, Kluwer, Academic Press, Dordrecht, 1989. [4] Z. Hu, M.S. Monfared and T. Traynor, On character amenable Banach algebras, Studia Math. 193 (2009), 53–78. [5] A. Mahmoodi, On ϕ-Connes amenability for dual Banach algebras, J. Linear Topol. Alg. 3 (2014), 211–217. [6] R. Nasr-Isfahani and S. Soltani Renani, Character contractibility of Banach algebras and homological properties of Banach modules, Stud. Math. 202 (2011), no. 3, 205–225. [7] M. Ramezanpour, Character Connes amenability of dual Banach algebras, Czech Math. J. 68 (2018), 243–255. [8] P. Ramsden, Biflatness of semigroup algebras, Semigroup Forum 79 (2009), 515–530. [9] V. Runde, Amenability for dual Banach algebras, Studia Math. 148 (2001), 47–66. [10] V. Runde, Dual Banach algebras: Connes-amenability, normal, virtual diagonals, and injectivity of the predual bimodule, Math. Scand. 95 (2004), 124–144. [11] V. Runde, Lectures on amenability, Lecture Notes in Mathematics, Vol. 1774, Springer-Verlag, Berlin, 2002. [12] A. Sahami, Left ϕ-biprojectivity of some Banach algebras, https://arxiv.org/abs/1905.05556 (2019). [13] A. Sahami, On biflatness and ϕ-bifltness of some Banach algebras, U.P.B. Sci. Bull. Ser. A 80 (2018), no. 1, 111–122. [14] A. Sahami and A. Pourabbas, On ϕ-biflat and ϕ-biprojective Banach algebras, Bull. Belg. Math. Soc. Simon Stevin 20 (2013), 789–801. [15] S.F. Shariati, A. Pourabbas and A. Sahami, On connes amenability of upper triangular matrix algebras, U.P.B. Sci. Bull. Series A 80 (2018), no. 2, 145–152. [16] S.F. Shariati, A. Pourabbas and A. Sahami, WAP-biprojectivity of the enveloping dual Banach algebras, Boll. Unione Mat. Ital. https://doi.org/10.1007/s40574-019-00205-9(2019). [17] A. Shirinkalam and A. Pourabbas, Connes-biprojective dual Banach algebras, U.P.B. Sci. Bull. Ser. A 78 (2016), no. 3, 175–184. | ||
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