Pseudo-amenability and pseudo-contractibility for certain products of Banach algebras
-
Eghbal Ghaderi
,
Rasoul Nasr-Isfahani
und
Mehdi Nemati
Abstract
Let 𝔄 and 𝔅 be two Banach algebras and let θ be 𝔄 nonzero character on 𝔅. In this paper, we deal with the θ-Lau product 𝔄 ×θ𝔅 that was first introduced by A. T. Lau for certain Banach algebras known as Lau algebras and recently by M. S. Monfared for all Banach algebras; we study pseudo-amenability, pseudo-contractibility and character pseudo-amenability of 𝔄 ×θ𝔅 and their relations with 𝔄 and 𝔅.
The second author’s research was supported in part by a grant from IPM (No. 92430417).
The third author research was supported in part by a grant from IPM (No. 92470046).
Acknowledgement
The authors would like to thank the referee of this paper for his thoughtful comments and useful suggestions. They acknowledge that this research was partially carried out at the IPM-Isfahan Branch.
References
[1] Alaghmandan, M.—Nasr-Isfahani, R.—Nemati, M.: On φ-contractibility of the Lebesgue-Fourier a lgebra of a locally compact group, Arch. Math. (Basel) 95 (2010), 373–37910.1007/s00013-010-0177-2Suche in Google Scholar
[2] Choi, Y.—Ghahramani, F.—Zhang, Y.: Approximate and pseudo-amenability of various classes of B anach algebras, J. Funct. Anal. 256 (2009), 3158–319110.1016/j.jfa.2009.02.012Suche in Google Scholar
[3] Dales, H. G.—LOY, R. J.—Zhang, Y.: Approximate amenability for Banach sequence algebras, Studia Math. 177 (2006), 81–9610.4064/sm177-1-6Suche in Google Scholar
[4] Desaulniers, S.—Nasr-Isfahani, R.—Nemati, M.: Common fixed point properties and amenability o f a class of Banach algebras, J. Math. Anal. Appl. 402 (2013), 536–54410.1016/j.jmaa.2012.12.057Suche in Google Scholar
[5] Ebrahimi Vishki, H. R.—Khoddami, A. R.: Character inner amenability of certain Banach algebras, Colloq. Math. 122 (2011), 225–23210.4064/cm122-2-7Suche in Google Scholar
[6] Ghaderi, E.—Nasr-Isfahani, R.—Nemati, M.: Some notions of amenability for certain products of B anach algebras, Colloq. Math. 130 (2013), 147–15710.4064/cm130-2-1Suche in Google Scholar
[7] Ghahramani, F.—Zhang, Y.: Pseudo-amenable and pseudo-contractible Banach algebras, Math. Proc. Camb. Phil. Soc. 142 (2007), 111–12310.1017/S0305004106009649Suche in Google Scholar
[8] Johnson, B. E.: Approximate diagonals and cohomology of certain annihilator Banach algebras, Amer. J. Math. 94 (1972), 685-69810.2307/2373751Suche in Google Scholar
[9] Johnson, B. E.: Cohomology in Banach algebras, Mem. Amer. Math. Soc. 127 (1972)10.1090/memo/0127Suche in Google Scholar
[10] Kaniuth, E.—Lau, A. T.—Pym, J.: On character amenability of Banach algebras, J. Math. Anal. Appl. 344 (2008), 942–95510.1016/j.jmaa.2008.03.037Suche in Google Scholar
[11] Kaniuth, E.—Lau, A. T.—Pym, J.: On ϕ-amenability of Banach algebras, Math. Proc. Camb. Phil. Soc. 144 (2008), 85–9610.1017/S0305004107000874Suche in Google Scholar
[12] Lau, A. T.: Analysis on a class of Banach algebras with application to Harmonic analysis on locally compact g roups and semigroups, Fund. Math. 118 (1983), 161–17510.4064/fm-118-3-161-175Suche in Google Scholar
[13] Lau, A. T.—Ludwig, J.: Fourier-Stieltjes algebra of a topological group, Advances in Math. 229 (2012), 2000–202310.1016/j.aim.2011.12.022Suche in Google Scholar
[14] Lau, A. T.—Wong, J. C. S.: Invariant subspaces for algebras of linear operators and amenable locally c ompact groups, Proc. Amer. Math. Soc. 102 (1988), 581–58610.1090/S0002-9939-1988-0928984-8Suche in Google Scholar
[15] Monfared, M. S.: Character amenability of Banach algebras, Math. Proc. Camb. Phil. Soc. 144 (2008), 697–70610.1017/S0305004108001126Suche in Google Scholar
[16] Monfared, M. S.: On certain products of Banach algebras with applications to Harmonic analysis, Studia Math. 178 (2007), 277–29410.4064/sm178-3-4Suche in Google Scholar
[17] Nasr-Isfahani, R.—Nemati, M.: Character pseudo-amenability of Banach algebras, Colloq. Math. (2013), to appear10.4064/cm132-2-2Suche in Google Scholar
[18] Nasr-Isfahani, R.—Nemati, M.: Cohomological characterizations of character pseudo-amenable Banach a lgebras, Bull. Austral. Math. Soc. 84, (2011), 229–23710.1017/S0004972711002267Suche in Google Scholar
[19] Nasr-Isfahani R.—Soltani Renani, S.: Character contractibility of Banach algebras and homological p roperties of Banach modules, Studia. Math. 202 (2011), 205–22510.4064/sm202-3-1Suche in Google Scholar
[20] Pier, J. P.: Amenable Banach algebras, Pitman Res. Notes Math. Ser. 172, Lonman, Harlow, 1988Suche in Google Scholar
[21] Pourabbas, A.—Nasrabadi, E.: Weak module amenability of triangular Banach algebras, Math. Slovaca 61 (2011), 949–958. Received8.12. 201310.2478/s12175-011-0061-ySuche in Google Scholar
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- A triple representation of lattice effect algebras
- Periods of morgan-voyce sequences and elliptic curves
- Multiplicative generalized derivations on ideals in semiprime rings
- A few remarks on Poincaré-Perron solutions and regularly varying solutions
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- Pseudo-amenability and pseudo-contractibility for certain products of Banach algebras
- Poisson kernels on semi-direct products of abelian groups
- Locally convex projective limit cones
- On the properties (wL) and (wV)
- On the existence of solutions for quadratic integral equations in Orlicz spaces
- Existence and uniqueness of best proximity points under rational contractivity conditions
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- On the internal approach to differential equations 3. Infinitesimal symmetries
- A Characterization of the discontinuity point set of strongly separately continuous functions on products
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