Johnson Pseudo-Contractibility and Pseudo-Amenability of $ theta $-Lau Product
Download PDF
Authors: M. ASKARI-SAYAH, A. POURABBAS AND A. SAHAMI
DOI: 10.46793/KgJMat2004.593A
Abstract:
Given Banach algebras A and B and ???? ∈ Δ(B). We shall study the Johnson pseudo-contractibility and pseudo-amenability of the ????-Lau product A ×????B. We show that if A ×????B is Johnson pseudo-contractible, then both A and B are Johnson pseudo-contractible and A has a bounded approximate identity. In some particular cases, a complete characterization of Johnson pseudo-contractibility of A ×????B is given. Also, we show that pseudo-amenability of A ×????B implies the approximate amenability of A and pseudo-amenability of B.
Keywords:
????-Lau product, Johnson pseudo-contractibility, pseudo-amenability.
References:
[1] M. Alaghmandan, Approximate amenability of Segal algebras, J. Aust. Math. Soc. 95(1) (2013), 20–35.
[2] M. Askari-Sayah, A. Pourabbas and A. Sahami, Johnson pseudo-contractibility of certain Banach algebras and their nilpotent ideals, Analysis Mathematica (to appear).
[3] Y. Choi, Triviality of the generalised Lau product associated to a Banach algebra homomorphism, Bull. Aust. Math. Soc. 94(2) (2016), 286–289.
[4] H. G. Dales, Banach Algebras and Automatic Continuity, London Mathematical Society Monographs, New Series 24, The Clarendon Press, Oxford University Press, New York, 2000.
[5] H. G. Dales, A. T. M. Lau and D. Strauss, Banach Algebras on Semigroups and on Their Compactifications, Memoirs of the American Mathematical Society 205(996), American Mathematical Society, Providence, 2010.
[6] H. G. Dales, R. J. Loy, and Y. Zhang, Approximate amenability for Banach sequence algebras, Studia Math. 177(1) (2006), 81–96.
[7] J. Duncan and A. L. T. Paterson, Amenability for discrete convolution semigroup algebras, Math. Scand. 66(1) (1990), 141–146.
[8] G. H. Esslamzadeh, Double centralizer algebras of certain Banach algebras, Monatsh. Math. 142(3) (2004), 193–203.
[9] B. Forrest and V. Runde, Amenability and weak amenability of the Fourier algebra, Math. Z. 250(4) (2005), 731–744.
[10] E. Ghaderi, R. Nasr-Isfahani and M. Nemati, Pseudo-amenability and pseudo-contractibility for certain products of Banach algebras, Math. Slovaca 66(6) (2016), 1367–1374.
[11] F. Ghahramani and R. J. Loy, Generalized notions of amenability, J. Funct. Anal. 208(1) (2004), 229–260.
[12] F. Ghahramani, R. J. Loy and Y. Zhang, Generalized notions of amenability II, J. Funct. Anal. 254(7) (2008), 1776–1810.
[13] F. Ghahramani and Y. Zhang, Pseudo-amenable and pseudo-contractible Banach algebras, Math. Proc. Cambridge Philos. Soc. 142(1) (2007), 111–123.
[14] A. Lau, Analysis on a class of Banach algebras with applications to harmonic analysis on locally compact groups and semigroups, Fund. Math. 118(3) (1983), 161–175.
[15] M. Monfared, On certain products of Banach algebras with applications to harmonic analysis, Studia Math. 178(3) (2007), 277–294.
[16] P. Ramsden, Biflatness of semigroup algebras, Semigroup Forum 79(3) (2009), 515–530.
[17] M. Rostami, A. Pourabbas and M. Essmaili, Approximate amenability of certain inverse semigroup algebras, Acta Math. Sci. Ser. B Engl. Ed. 33(2) (2013), 565–577.
[18] V. Runde, Amenability for dual Banach algebras, Studia Math. 148(1) (2001), 47–66.
[19] A. Sahami and A. Pourabbas, Johnson pseudo-contractibility of various classes of Banach algebras, Bull. Belg. Math. Soc. Simon Stevin 25(2) (2018), 171–182.
[20] A. Sahami and A. Pourabbas, Johnson pseudo-contractibility of certain semigroup algebras, Semigroup Forum 97(2) (2018), 203–213.
Login:
