A notion of approximate biflatness for Banach algebras based on character space. (English) Zbl 1518.46049
Summary: The notion of approximate left \(\phi\)-biflatness for Banach algebras is introduced, where \(\phi :A\longrightarrow \mathbb{C}\) is a non-zero multiplicative linear functional. Under this new concept, the approximate left \(\phi\)-biflatness for some algebras like group algebras and measure algebras are studied. Moreover, some hereditary properties of this notion are given. Furthermore, some examples to show the differences of our notion and the classical ones are presented.
MSC:
| 46M10 | Projective and injective objects in functional analysis |
| 43A20 | \(L^1\)-algebras on groups, semigroups, etc. |
| 46H05 | General theory of topological algebras |
References:
| [1] | Aghababa, HP; Shi, LY; Wu, YJ, Generalized notions of character amenability, Acta Math. Sin. (Engl. Ser.), 29, 7, 1329-1350 (2013) · Zbl 1280.46031 · doi:10.1007/s10114-013-0627-4 |
| [2] | Bodaghi, A., Amini, M.: Module biprojective and module biflat Banach algaebras, U.P.B. Sci. Bull. Series A., 75 Iss. 3, 25-36, (2013) · Zbl 1299.43002 |
| [3] | Bodaghi, A.; Ebrahimi, H.; Lashkarizaheh Bami, M., Generalized notions of module character amenability, Filomat, 31, 6, 1639-1654 (2017) · Zbl 1488.22006 · doi:10.2298/FIL1706639B |
| [4] | Bodaghi, A.; Grailoo Tanha, S., Module approximate biprojectivity and module approximate bifatness of Banach algebras, Rend. del Cir. Mat. di Palermo Series 2,, 70, 409-425 (2021) · Zbl 1469.46073 · doi:10.1007/s12215-020-00503-8 |
| [5] | Ghahramani, F.; Zhang, Y., Pseudo-amenable and pseudo-contractible Banach algebras, Math. Proc. Cambridge Philos. Soc., 142, 111-123 (2007) · Zbl 1118.46046 · doi:10.1017/S0305004106009649 |
| [6] | Ghorbani, ZG; Bami, ML, \( \phi \)-Approximate biflat and \(\phi \)-amenable Banach algebras, Proc. Romanian Acad. -Series A: Math. Phy. Tech. Sci., Inf.Sci.,, 13, 3-10 (2012) · Zbl 1324.46061 |
| [7] | Helemskii, AY, The Homology of Banach and Topological Algebras (1986), Dordrecht: Kluwer Academic Publishers, Dordrecht |
| [8] | Johnson, B.E.: Cohomology in Banach Algebras. Memoirs Amer. Math. Soc., No. 127. American Mathematical Society, Providence (1972) · Zbl 0256.18014 |
| [9] | Kaniuth, E.; Lau, AT; Pym, J., On \(\phi \)-amenability of Banach algebras, Math. Proc. Camb. Philos. Soc., 44, 85-96 (2008) · Zbl 1145.46027 · doi:10.1017/S0305004107000874 |
| [10] | Kotzmann, E.; Rindler, H., Segal algebras on non-abelian groups, Trans. Amer. Math. Soc., 237, 271-281 (1978) · Zbl 0363.43004 · doi:10.1090/S0002-9947-1978-0487277-4 |
| [11] | Nasr-Isfahani, R.; Nemati, M., Character pseudo-amenability of Banach algebras, Colloquium Math., 132, 177-193 (2013) · Zbl 1290.43006 · doi:10.4064/cm132-2-2 |
| [12] | Runde, V., Lectures on Amenability (2002), New York: Springer, New York · Zbl 0999.46022 · doi:10.1007/b82937 |
| [13] | A. Sahami, On left \(\phi \)-biflatness and \(\phi \)-biprojective Banach algebras, U.P.B. Sci. Bull., Series A, 81 (2019), Iss. 4 , 97-106 · Zbl 1513.46140 |
| [14] | Sahami, A.; Rostami, M.; Pourabbas, A., On left \(\phi \)-biflat Banach algebras, Comment Mat. Car., 61, 3, 337-344 (2020) · Zbl 1538.46088 |
| [15] | Samei, E.; Spronk, N.; Stokke, R., Biflatness and pseudo-amenability of Segal algebras, Canad. J. Math., 62, 845-869 (2010) · Zbl 1201.43002 · doi:10.4153/CJM-2010-044-4 |
| [16] | Sangani Monfared, M., Character amenability of Banach algebras, Math. Proc. Camb. Philos. Soc., 144, 697-706 (2008) · Zbl 1153.46029 · doi:10.1017/S0305004108001126 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
