Approximate ideal connes amenability of dual Banach algebras and ideal connes amenability of discrete Beurling algebras
Eurasian mathematical journal, Tome 11 (2020) no. 2, pp. 72-85.

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The concept of approximate Connes amenability of dual Banach algebras was introduced in [9]. In this paper we introduce approximate ideal Connes amenability for dual Banach algebras. We show that every approximate Connes amenable dual Banach algebra is approximate ideally Connes amenable. The notion of ideal Connes amenability for dual Banach algebras was introduced in [14]. In this paper we also study ideal Connes amenability for discrete Beurling algebras.
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A. Minapoor. Approximate ideal connes amenability of dual Banach algebras and ideal connes amenability of discrete Beurling algebras. Eurasian mathematical journal, Tome 11 (2020) no. 2, pp. 72-85. http://geodesic.mathdoc.fr/item/EMJ_2020_11_2_a7/

[1] Y. Choi, E. Samei, R. Stokke, Extension of derivations, and Connes amenability of enveloping dual Banach algebra, 17 June 2014, arXiv: 1307.6287v2 [math.FA] | MR

[2] H. G. Dales, Banach algebras, automatic continuty, Oxford Uinversity Press, 2000 | MR

[3] H. G. Dales, F. Ghahramani, A. Helemskii, “The amenability of measure algebras”, J. London Math. Soc., 66 (2002), 213–226 | MR | Zbl

[4] M. Daws, “Connes amenability of bidual and weighted semigroup algebras”, Math. Scand., 99 (2006), 217–246 | MR | Zbl

[5] M. M. Day, “Means on semigroups and groups”, Bull. Amer. Math. Soc., 55 (1949), 1054–1055

[6] U. Haagerup, “All nuclear C-algebras are amenable”, Invent. Math., 74 (1983), 305–319 | MR | Zbl

[7] E. G. Effros, “Amenability and virtual diagonals for von Neumann algebras”, J. Funct. Anal., 78 (1988), 137–156 | MR

[8] M. Eshaghi Gordji, T. Yazdanpanah, “Derivations into duals of ideals of Banach algebras”, Proc. Ind. Acad. Sci. (Math. Sci.), 114:4 (2004), 399–408 | MR | Zbl

[9] G. H. Esslamzadeh, B. Shojaee, Approximate Connes amenability of dual Banach algebras, 24 Jan 2011, arXiv: 0908.3566v2 [math.FA] | MR

[10] N. Grqnbaek, “Amenability of weighted discrete convolution algebras on cancellative semigroup”, Proc. Roy. Soc. Edinburgh Sect. A, 110 (1988), 351–360 | MR

[11] B. E. Johnson, Cohomology in Banach algebras, Memoirs of the American Mathematical Society, 127, American Mathematical Soc., 1972, 96 pp. | MR | Zbl

[12] B. E. Johnson, R. V. Kadison, J. R. Ringrose, “Cohomology of operator algebras III”, Bull. Soc. Math. Fr., 100 (1972), 73–96 | MR | Zbl

[13] J. L. Kelly, General topology, American Book, Von Nostrand Reinhold, 1968

[14] A. Minapoor, A. Bodaghi, D. Ebrahimi Bagha, “Ideal Connes-amenability of dual Banach algebras”, Mediterr. J. Math., 14:174 (2017) | DOI | MR | Zbl

[15] S. Naseri, “Approximate amenability of weighted group algebras”, International Mathematical Forum, 6:2 (2011), 49–56 | MR | Zbl

[16] V. Runde, “A Connes-amenable, dual Banach algebra need not have a normal, virtual diagonal”, Trans. Amer. Math. Soc., 358:1 (2005), 391–402 | MR

[17] V. Runde, “Amenability for dual Banach algebras”, Studia Math., 148 (2001), 47–66 | MR | Zbl

[18] V. Runde, Lectures on amenability, Lecture Notes in Mathematics, 1774, Springer-Verlag, Berlin–Heidelberg–New York, 2002 | MR | Zbl

[19] V. Runde, “Connes-amenability and normal, virtual diagonals for measure algebras (II)”, Bull. Austral. Math. Soc., 68 (2003), 325–328 | MR | Zbl

[20] V. Shepelska, Weak amenability of weighted group algebras and of their centres, PhD. thesis, University of Manitoba, 2014 http://hdl.handle.net/1993/24313

[21] A. Shirinkalam, A. Pourabbas, On approximate Connes amenability of enveloping dual Banach algebras, 24 January 2015, arXiv: 1501.06028v1 [math.FA] | MR | Zbl

[22] J. Von Neumann, “Zur allgemeinen theories des maßes”, Fund. Math., 13 (1929), 73–116 | Zbl

[23] Y. Zhang, “Weak amenability of commutative beurling algebras”, Proc. Amer. Math. Soc., 142 (2014), 1649–1661 | MR | Zbl