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http://dx.doi.org/10.5831/HMJ.2019.41.4.697

(𝜑, 𝜓)-BIFLAT AND 𝜑, 𝜓)-AMENABLE BANACH ALGEBRAS  

Baradara, Javad (Department of Mathematics, Jahrom University)
Ghorbani, Zahra (Department of Mathematics, Jahrom University)
Publication Information
Honam Mathematical Journal / v.41, no.4, 2019 , pp. 697-705 More about this Journal
Abstract
The article studies the concept of a (𝜑, 𝜓)-biflat and (𝜑, 𝜓)-amenable Banach algebra A, where 𝜑 is a continuous homomorphism on A and 𝜓 ∈ ΦA. We show if A has a (𝜑, 𝜓)-virtual diagonal, then A is (𝜑, 𝜓)- biflat. In the case where 𝜑(A) is commutative we prove that (𝜑, 𝜓)- biflatness of A implies that A has a (𝜑, 𝜓)-virtual diagonal.
Keywords
Banach algebra; (${\varphi}$, ${\psi}$)-amenable; (${\varphi}$, ${\psi}$)-biflat;
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  • Reference
1 M. Ashraf and N.Rehman, On (${\sigma}-{\tau}$) derivations in prime rings, Arch. Math. (BRNO) 38 (2002), 259 - 264.
2 F. F. Bonsall and J. Duncan, Complete normed algebra, Springer-Verlag, 1973.
3 H. G. Dales, Banach algebras and automatic continuity, London Mathematical Society Monographs 24 (Clarendon Press, Oxford), 2000.
4 A. Ya. Helemskii, Banach and locally convex algebras, Clarendon Press, Oxford University Press, New York, 1993.
5 A. Ya. Helemskii, Flat Banach modules and amenable algebras, (translated from the Russian). Trans. Moscow Math. Soc. 47 (1985), 199-224.
6 A. Ya. Helemskii, The Homology of Banach and topological algebras, 41 of Mathematics and its Applications (Soviet Series), Kluwer Academic Publishers Group, Dordrecht, 1989.
7 B. E. Johnson, Cohomology in Banach algebras, Mem. Amer. Math. Soc., 1972.
8 M. Mirzavaziri and M.S. Moslehian, ${\sigma}$-derivations in Banach algebras, Bull. Iranian Math. Soc. (2006), 65-78.
9 E. Kaniuth, A. Lau, and J. Pym, On ${\varphi}$-amenability of Banach algebras, Math. Proc. Camb. Phil. Soc. 144 (2008), 85-96.   DOI
10 J. L. Kelley, General topology, D. Van Nostrand Company, Inc., New York, 1955.
11 M. S. Moslehian and A. N. Motlagh, Some notes on (${\sigma},{\tau}$)-amenability of Banach algebras, Stud. Univ. Babes-Bolyai Math. 53 (2008), 57-68.
12 P. Ramsden, Biflatness of semigroup algebras, Semigroup Forum, 79 (2009), 515-530.   DOI
13 V. Runde, Lectures on Amenability, Lecture Notes in Mathematics 1774, Springer, 2002.