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Keywords:
upper triangular Banach algebra; amenability; left $\varphi$-amenability; approximate biprojectivity
upper triangular Banach algebra; amenability; left $\varphi$-amenability; approximate biprojectivity
Summary:
We investigate the amenability and its related homological notions for a class of $I\times I$-upper triangular matrix algebra, say ${\rm UP}(I,A)$, where $A$ is a Banach algebra equipped with a nonzero character. We show that ${\rm UP}(I,A)$ is pseudo-contractible (amenable) if and only if $I$ is singleton and $A$ is pseudo-contractible (amenable), respectively. We also study pseudo-amenability and approximate biprojectivity of ${\rm UP}(I,A)$.
References:
[1] Aghababa H. P., Shi L. Y., Wu Y. J.: Generalized notions of character amenability. Acta Math. Sin. (Engl. Ser.) 29 (2013), no. 7, 1329–1350. DOI 10.1007/s10114-013-0627-4 | MR 3068583
[2] Alaghmandan M., Nasr-Isfahani R., Nemati M.: On $\phi$-contractibility of the Lebesgue-Fourier algebra of a locally compact group. Arch. Math. (Basel) 95 (2010), no. 4, 373–379. DOI 10.1007/s00013-010-0177-2 | MR 2727314
[3] Choi Y., Ghahramani F., Zhang Y.: Approximate and pseudo-amenability of various classes of Banach algebras. J. Funct. Anal. 256 (2009), no. 10, 3158–3191. DOI 10.1016/j.jfa.2009.02.012 | MR 2504522
[4] Dashti M., Nasr-Isfahani R., Soltani Renani S.: Character amenability of Lipschitz algebras. Canad. Math. Bull. 57 (2014), no. 1, 37–41. DOI 10.4153/CMB-2012-015-3 | MR 3150714
[5] Dales H. G., Lau A. T.-M., Strauss D.: Banach algebras on semigroups and on their compactifications. Mem. Amer. Math. Soc. 205 (2010), no. 966, 165 pages. MR 2650729
[6] Duncan J., Paterson A. L. T.: Amenability for discrete convolution semigroup algebras. Math. Scand. 66 (1990), no. 1, 141–146. DOI 10.7146/math.scand.a-12298 | MR 1060904
[7] Esslamzadeh G. H.: Double centralizer algebras of certain Banach algebras. Monatsh. Math. 142 (2004), no. 3, 193–203. DOI 10.1007/s00605-003-0046-1 | MR 2071245
[8] Forrest B. E., Marcoux L. W.: Derivations of triangular Banach algebras. Indiana. Univ. Math. J. 45 (1996), no. 2, 441–462. DOI 10.1512/iumj.1996.45.1147 | MR 1414337
[9] Forrest B. E., Marcoux L. W.: Weak amenability of triangular Banach algebras. Trans. Amer. Math. Soc. 354 (2002), no. 4, 1435–1452. DOI 10.1090/S0002-9947-01-02957-9 | MR 1873013
[10] Ghahramani F., Loy R. J.: Generalized notions of amenability. J. Funct. Anal. 208 (2004), no. 1, 229–260. DOI 10.1016/S0022-1236(03)00214-3 | MR 2034298
[11] Ghahramani F., Loy R. J., Zhang Y.: Generalized notions of amenability. II. J. Funct. Anal. 254 (2008), no. 7, 1776–1810. DOI 10.1016/j.jfa.2007.12.011 | MR 2397875
[12] Ghahramani F., Zhang Y.: Pseudo-amenable and pseudo-contractible Banach algebras. Math. Proc. Cambridge Philos. Soc. 142 (2007), no. 1, 111–123. DOI 10.1017/S0305004106009649 | MR 2296395 | Zbl 1118.46046
[13] 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
[14] Jabbari A., Abad T. M., Abadi M. Z.: On $\phi$-inner amenable Banach algebras. Colloq. Math. 122 (2011), no. 1, 1–10. DOI 10.4064/cm122-1-1 | MR 2755887
[15] 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
[16] Nasr-Isfahani R., Soltani Renani S.: Character contractibility of Banach algebras and homological properties of Banach modules. Studia Math. 202 (2011), no. 3, 205–225. DOI 10.4064/sm202-3-1 | MR 2771651
[17] Runde V.: Lectures on Amenability. Lecture Notes in Mathematics, 1774, Springer, Berlin, 2002. MR 1874893
[18] Sahami A., Pourabbas A.: Approximate biprojectivity of certain semigroup algebras. Semigroup Forum 92 (2016), no. 2, 474–485. DOI 10.1007/s00233-015-9701-9 | MR 3472027
[19] Sahami A.: On biflatness and $\phi$-biflatness of some Banach algebras. Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys. 80 (2018), no. 1, 111–122. MR 3785185
[20] Sahami A., Pourabbas A.: On $\phi$-biflat and $\phi$-biprojective Banach algebras. Bull. Belg. Math. Soc. Simon Stevin 20 (2013), no. 5, 789–801. DOI 10.36045/bbms/1385390764 | MR 3160589
[21] Zhang Y.: Nilpotent ideals in a class of Banach algebras. Proc. Amer. Math. Soc. 127 (1999), no. 11, 3237–3242. DOI 10.1090/S0002-9939-99-04896-0 | MR 1605957
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