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left $\varphi$-biflat; Segal algebra; semigroup algebra; locally compact group
We study the notion of left $\varphi$-biflatness for Segal algebras and semigroup algebras. We show that the Segal algebra $S(G)$ is left $\varphi$-biflat if and only if $G$ is amenable. Also we characterize left $\varphi$-biflatness of semigroup algebra $l^{1}(S)$ in terms of biflatness, when $S$ is a Clifford semigroup.
[1] Alaghmandan M., Nasr-Isfahani R., Nemati M.: Character amenability and contractibility of abstract Segal algebras. Bull. Aust. Math. Soc. 82 (2010), no. 2, 274–281. DOI 10.1017/S0004972710000286 | MR 2685151
[2] Essmaili M., Rostami M., Amini M.: A characterization of biflatness of Segal algebras based on a character. Glas. Mat. Ser. III 51(71) (2016), no. 1, 45–58. DOI 10.3336/gm.51.1.04 | MR 3516184
[3] Ghahramani F., Lau A. T. M.: Weak amenability of certain classes of Banach algebra without bounded approximate identities. Math. Proc. Cambridge Philos. Soc. 133 (2002), no. 2, 357–371. DOI 10.1017/S0305004102005960 | MR 1912407
[4] Ghahramani F., Loy R. J., Willis G. A.: Amenability and weak amenability of second conjugate Banach algebras. Proc. Amer. Math. Soc. 124 (1996), no. 5, 1489–1497. DOI 10.1090/S0002-9939-96-03177-2 | MR 1307520
[5] Hewitt E., Ross K. A.: Abstract Harmonic Analysis I: Structure of Topological Groups. Integration Theory, Group Representations. Die Grundlehren der mathematischen Wissenschaften, 115, Academic Press, Springer, Berlin, 1963. MR 0156915
[6] Howie J. M.: Fundamental of Semigroup Theory. London Mathematical Society Monographs, New Series, 12, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1995. MR 1455373
[7] Hu Z., Monfared M. S., Traynor T.: On character amenable Banach algebras. Studia Math. 193 (2009), no. 1, 53–78. DOI 10.4064/sm193-1-3 | MR 2506414
[8] Javanshiri H., Nemati M.: Invariant $\varphi$-means for abstract Segal algebras related to locally compact groups. Bull. Belg. Math. Soc. Simon Stevin 25 (2018), no. 5, 687–698. DOI 10.36045/bbms/1547780429 | MR 3901840
[9] Kaniuth E., Lau A. T., Pym J.: On $\phi$-amenability of Banach algebras. Math. Proc. Cambridge Philos. Soc. 144 (2008), no. 1, 85–96. DOI 10.1017/S0305004107000874 | MR 2388235
[10] Ramsden P.: Biflatness of semigroup algebras. Semigroup Forum 79 (2009), no. 3, 515–530. DOI 10.1007/s00233-009-9169-6 | MR 2564061
[11] Reiter H.: $L^{1}$-algebras and Segal Algebras. Lecture Notes in Mathematics, 231, Springer, Berlin, 1971. MR 0440280
[12] Runde V.: Lectures on Amenability. Lecture Notes in Mathematics, 1774, Springer, Berlin, 2002. MR 1874893
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