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\(\varphi \)-biprojectivity of Banach algebras with applications to hypergroup algebras. (English) Zbl 1414.43006

In this paper, the authors study the notions of \(\varphi\)-biprojectivity and \(\varphi\)-Johnson contractibility of certain Banach algebras. In fact, they characterize \(\varphi\)-biprojectivity of hypergroup algebras. They show that the hypergroup algebra \(L^{1}(K)\) is \(\varphi\)-biprojective if and only if \(K\) is compact. Some results about the Segal algebras related to the hypergroup algebras are given.

MSC:

43A20 \(L^1\)-algebras on groups, semigroups, etc.
43A22 Homomorphisms and multipliers of function spaces on groups, semigroups, etc.
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[1] Azimifard, A.: On the amenability of compact and discrete hypergroup algebras (2009). ArXiv:0908.1590v2 [Math.FA]
[2] Bloom, W.R., Heyer, H.: Harmonic Analysis of probability measures on hypergroups. Walter de Gruyter, Berlin (1995) · Zbl 0828.43005 · doi:10.1515/9783110877595
[3] Dales, H.G.: Banach Algebras and Automatic Continuity. Oxford University Press, New York (2000) · Zbl 0981.46043
[4] Dunkl, C.F.: The measure algebra of a locally compact hypergroup. Trans. Am. Math. Soc. 179, 331-348 (1973) · Zbl 0241.43003 · doi:10.1090/S0002-9947-1973-0320635-2
[5] Essmaili, M., Rostami, M., Amini, M.: A characterization of biflatness of Segal algebras based on a character. Glasnik Math. 51, 45-58 (2016) · Zbl 1345.43003 · doi:10.3336/gm.51.1.04
[6] Helemskii, A.Ya.: The Homology of Banach and Topological Algebras. Kluwer Academic Publishers Group, Dordrecht (1989) · doi:10.1007/978-94-009-2354-6
[7] Hewitt, E., Ross, K.A.: Abstract harmonic analysis. Vol. II: Structure and analysis for compact groups. Analysis on locally compact Abelian groups. Springer, New York (1970) · Zbl 0213.40103
[8] Hu, Z., Monfared, M.S., Traynor, T.: On character amenable Banach algebras. Stud. Math. 193, 53-78 (2009) · Zbl 1175.22005 · doi:10.4064/sm193-1-3
[9] Jewett, R.I.: Spaces with an abstract convolution of measures. Adv. Math. 18, 1-101 (1975) · Zbl 0325.42017 · doi:10.1016/0001-8708(75)90002-X
[10] Kaniuth, E., Lau, A.T.M., Pym, J.: On \[\varphi\] φ-amenability of Banach algebras. Math. Proc. Camb. Philos. Soc. 144, 85-96 (2008) · Zbl 1145.46027 · doi:10.1017/S0305004107000874
[11] Kaniuth, E., Lau, A.T., Pym, J.S.: On character amenability of Banach algebras. J. Math. Anal. Appl. 344, 942-955 (2008) · Zbl 1151.46035 · doi:10.1016/j.jmaa.2008.03.037
[12] Lasser, R.: Various amenability properties of the \[l^1\] l1-algebra of polynomial hypergroups and applications. J. Comput. Appl. Math. 233, 786-792 (2009) · Zbl 1182.43008 · doi:10.1016/j.cam.2009.02.046
[13] Nasr-Isfahani, R., Soltani Renani, S.: Character contractibility of Banach algebras and homological properties of Banach modules. Stud. Math. 202, 205-225 (2011) · Zbl 1236.46045 · doi:10.4064/sm202-3-1
[14] Pourmahmood-Aghababa, H., Shi, L.Y., Wu, Y.J.: Generalized notions of character amenability. Acta Math. Sin. Engl. Ser. 29, 1329-1350 (2013) · Zbl 1280.46031 · doi:10.1007/s10114-013-0627-4
[15] Runde, V.: Lectures on amenability, Lecture Note in Mathematics 1774. Springer, Berlin (2002)
[16] Sahami, A., Pourabbas, A.: On \[\phi\] ϕ-biflat and \[\phi\] ϕ-biprojective Banach algebras. Bull. Belg. Math. Soc. Simon Stevin 20, 789-801 (2013) · Zbl 1282.43001
[17] Sahami, A., Pourabbas, A.: On character biprojectivity of Banach algebras. UPB Sci. Bull. Ser. A Appl. Math. Phys. 78, 163-174 (2016) · Zbl 1352.43003
[18] Skantharajah, M.: Amenable hypergroups. Illinois J. Math. 36, 15-46 (1992) · Zbl 0755.43003 · doi:10.1215/ijm/1255987605
[19] Vrem, R.C.: Harmonic analysis on compact hypergroups. Pac. J. Math. 85, 239-251 (1979) · Zbl 0458.43002 · doi:10.2140/pjm.1979.85.239
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