Document Type : Research Paper
Authors
- Hasan Pourmahmood Aghababa ^{1}
- Fourogh Khedri ^{2}
- Mohammad Hossein Sattari ^{} ^{2}
^{1} Department of Mathematics, University of Tabriz, Tabriz, Iran.
^{2} Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran.
Abstract
The bounded approximate version of $\varphi$-amenability and character amenability are introduced and studied. These new notions are characterized in several different ways, and some hereditary properties of them are established. The general theory for these concepts is also developed. Moreover, some examples are given to show that these notions are different from the others. Finally, bounded approximate character amenability of some Banach algebras related to locally compact groups are investigated.
Keywords
- Banach algebras
- Bounded approximate character amenability
- Bounded approximate character contractibility
- Locally compact groups
Main Subjects
[1] H.P. Aghababa, L.Y. Shi, and Y.J. Wu, Generalized notions of character amenability, Acta Math. Sin. (Engl. Ser.), 29 (2013), pp. 1329-1350.
[2] Y. Choi, F. Ghahramani, and Y. Zhang, Approximate and pseudo-amenability of various classes of Banach algebras, J. Funct. Anal., 256 (2009), pp. 3158-3191.
[3] B. Dorofaeff, The Fourier algebra of SL(2, R)?R^n, n≥2, has no multiplier bounded approximate unit, Math. Ann., 297 (1993), pp. 707-724.
[4] F. Ghahramani and R.J. Loy, Generalized notions of amenability, J. Funct. Anal., 208 (2004), pp. 229-260.
[5] F. Ghahramani, R.J. Loy, and Y. Zhang, Generalized notions of amenability II, J. Funct. Anal., 254 (2008), pp. 1776-1810.
[6] F. Ghahramani and C.J. Read, Approximate identities in approximate amenability, J. Funct. Anal., 262 (2012), pp. 3929-3945.
[7] U. Haagerup, An example of a nonnuclear $C^*$-algebra, which has the metric approximation property, Invent. math., 50 (1978/79), pp. 279-293.
[8] C. Herz, Harmonic synthesis for subgroups, Ann. Inst. Fourier (Grenoble), 23 (1973), pp. 91-123.
[9] Z. Hu, M.S. Monfared, and T. Traynor, On character amenable Banach algebras, Studia Math., 193 (2009), pp. 53-78.
[10] B.E. Johnson, Cohomology in Banach algebras, Mem. Amer. Math. Soc., 127 (1972), pp. 1-96.
[11] E. Kaniuth, A.T. Lau, and J. Pym, On character amenability of Banach algebras, J. Math. Anal. Appl., 344 (2008), pp. 942-955.
[12] M.S. Monfared, Character amenability of Banach algebras, Math. Proc. Cambridge Philos. Soc., 144 (2008), pp. 697-706.