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On biprojectivity and Connes biprojectivity of a dual Banach algebra with respect to a $w^*$ -closed ideal | ||
| AUT Journal of Mathematics and Computing | ||
| دوره 5، شماره 3، 2024، صفحه 225-231 اصل مقاله (412.49 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22060/ajmc.2023.22285.1149 | ||
| نویسندگان | ||
| Amir Sahami* 1؛ S. Fatemeh Shariati2؛ Mehdi Rostami2؛ Mona Aj3 | ||
| 1Department of Mathematics, Faculty of Basic Sciences, Ilam University, P.O. Box 69315-516, Ilam, Iran | ||
| 2Faculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Iran | ||
| 3Department of Mathematics, Farhangian University of Kermanshah, Kermanshah, Iran | ||
| چکیده | ||
| In this paper, we introduce a notion of Connes biprojectivity for a dual Banach algebra $A$ with respect to its $w^{*}$-closed ideal $I$, say $I$-Connes biprojectivity. Some Lipschitz algebras $Lip_{\alpha}(X)$ and some matrix algebras are studied under this new notion. Also, with some mild assumptions, the relation between $I$-Connes biprojectivity and left $\phi$-contractibility is given, where $\phi$ is a $w^{*}$-continuous multiplicative linear functional on $A$. As an application, we characterize Connes biprojectivity of some Lipschitz algebras. | ||
| کلیدواژه‌ها | ||
| $I$-Connes biprojctivity؛ Left $\phi$-contractibility؛ Dual Banach algebras | ||
| مراجع | ||
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[1]F. Abtahi, E. Byabani, and A. Rejali, Some algebraic and homological properties of Lipschitz algebras and their second duals, Arch. Math. (Brno), 55 (2019), pp. 211–224.
[2] W. G. Bade, P. C. Curtis, Jr., and H. G. Dales, Amenability and weak amenability for Beurling and Lipschitz algebras, Proc. London Math. Soc. (3), 55 (1987), pp. 359–377.
[3] F. Gourdeau, Amenability of Banach algebras, Math. Proc. Cambridge Philos. Soc., 105 (1989), pp. 351–355. 36 A. Sahami et al., AUT J. Math. Com., 6(1) (2024) 31-37, OI:10.22060/AJMC.2023.22285.1149
[4] A. Y. Helemskii, The homology of Banach and topological algebras, vol. 41 of Mathematics and its Applica[1]tions (Soviet Series), Kluwer Academic Publishers Group, Dordrecht, 1989. Translated from the Russian by Alan West.
[5] B. E. Johnson, Cohomology in Banach algebras, Memoirs of the American Mathematical Society, No. 127, American Mathematical Society, Providence, RI, 1972.
[6] E. Kaniuth, A. T. Lau, and J. Pym, On ϕ-amenability of Banach algebras, Math. Proc. Cambridge Philos. Soc., 144 (2008), pp. 85–96.
[7] A. Mahmoodi, φ-contractibility and φ-Connes amenability coincide with some older notions, Bull. Aust. Math. Soc., 97 (2018), pp. 274–278.
[8] A. Minapoor, A. Bodaghi, and D. Ebrahimi Bagha, Ideal Connes-amenability of dual Banach algebras, Mediterr. J. Math., 14 (2017), pp. Paper No. 174, 12.
[9] A. Minapoor and A. Zivari-Kazempour, Ideal Connes-amenability of certain dual Banach algebras, Com[1]plex Anal. Oper. Theory, 17 (2023), pp. Paper No. 27, 11.
[10] R. Nasr-Isfahani and S. Soltani Renani, Character contractibility of Banach algebras and homological properties of Banach modules, Studia Math., 202 (2011), pp. 205–225.
[11] V. Runde, Amenability for dual Banach algebras, Studia Math., 148 (2001), pp. 47–66.
[12] , Lectures on amenability, vol. 1774 of Lecture Notes in Mathematics, Springer-Verlag, Berlin, 2002.
[13] , Dual Banach algebras: Connes-amenability, normal, virtual diagonals, and injectivity of the predual bimodule, Math. Scand., 95 (2004), pp. 124–144.
[14] A. Sahami, M. Rostami, and S. Kalantari, On I-biflat and I-biprojective Banach algebras, Wavelet and Linear Algebra, 8 (2021), pp. 49–59.
[15] A. Sahleh and A. Z. Kazempour, Some results on Banach precompact elements of a locally convex algebra, Far East J. Math. Sci. (FJMS), 31 (2008), pp. 17–23.
[16] A. Shirinkalam and A. Pourabbas, Connes-biprojective dual Banach algebras, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys., 78 (2016), pp. 175–184 | ||
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