In this note, we show that [11, Corollary 3.2] is not always true. In fact, we characterize essential left ϕ-contractibility of group algebras in terms of compactness of its related locally compact group. Also, we show that for any compact commutative group G, L2(G) is always essentially left ϕ-contractible. We discuss the essential left ϕ-contractibility of some Fourier algebras.
M. Alaghmandan, R. Nasr Isfahani and M. Nemati, Character amenability and contractibility of abstract Segal algebras, Bull. Austral. Math. Soc., 82: 274–281, (2010).
F. Ghahramani and R.J. Loy, Generalized notions of amenability, J. Func. Anal., 208: 229–260, (2004).
E. Hewitt and K.A. Ross, Abstract Harmonic Analysis I, Springer-Verlag, Berlin, (1963).
E. Kaniuth and A.T. Lau, Fourier and Fourier Stieltjes Algebras on Locally Compact Groups, Amer. Math. Soc., Vol 231, (2018).
E. Kaniuth, A.T. Lau and J. Pym, On ϕ-amenability of Banach algebras, Math. Proc. Cambridge Philos. Soc., 144: 85–96, (2008).
R. Nasr Isfahani and M. Nemati, Essential character amenability of Banach algebras, Bull. Austral. Math. Soc., 84: 372–386, (2011).
R. Nasr Isfahani and S. Soltani Renani, Character contractibility of Banach algebras and homological properties of Banach modules, Studia Math., 202(3): 205–225, (2011).
M. Nemati, Some homological properties of Banach algebras associated with locally compact groups, Colloq. Math., 139: 259–271, (2015).
W. Rudin, Fourier Analysis on Groups, Interscience Publishers, New York - London, (1962).
V. Runde, Lectures on amenability, Springer, New York, (2002).
R. Sadheghi Nahrekhalaji, Essential character contractibility for Banach algebras,U.P.B. Sci. Bull., Series A., 81(2): 165–176, (2019).
M. Sangani Monfared, Character amenability of Banach algebras, Math. Proc. Camb. Phil. Soc., 144: 697-706, (2008).
Y. Zhang, Nilpotent ideals in a class of Banach algebras, Proc. Amer. Math. Soc., 127(11): 3237-3242, (1999).
Sahami, A., & Almasi, I. (2020). A Note on Essentially Left ϕ-Contractible Banach Algebras. Analytical and Numerical Solutions for Nonlinear Equations, 5(1), 23-27. doi: 10.22128/gadm.2020.355.1027
MLA
Amir Sahami; Isaac Almasi. "A Note on Essentially Left ϕ-Contractible Banach Algebras", Analytical and Numerical Solutions for Nonlinear Equations, 5, 1, 2020, 23-27. doi: 10.22128/gadm.2020.355.1027
HARVARD
Sahami, A., Almasi, I. (2020). 'A Note on Essentially Left ϕ-Contractible Banach Algebras', Analytical and Numerical Solutions for Nonlinear Equations, 5(1), pp. 23-27. doi: 10.22128/gadm.2020.355.1027
VANCOUVER
Sahami, A., Almasi, I. A Note on Essentially Left ϕ-Contractible Banach Algebras. Analytical and Numerical Solutions for Nonlinear Equations, 2020; 5(1): 23-27. doi: 10.22128/gadm.2020.355.1027
)
