Document Type : Research Paper
Authors
Department of Mathematics, Semnan University, P.O.Box 35195-363, Semnan, Iran.
Abstract
We introduce the notions of $\mathcal{T}_{M}$-amenability and $\phi$-$\mathcal{T}_{M}$-amenability. Then, we characterize $\phi$-$\mathcal{T}_{M}$-amenability in terms of $WAP$-diagonals and $\phi$-invariant means. Some concrete cases are also discussed.
Keywords
Main Subjects
1. C. Akemann, The dual space of an operator algebra, Trans. Amer. Math. Soc., 126 (1967), pp. 286-302.
2. C. Akemann, Some mapping properties of the group algebras of a compact group, Pacific Journal of Mathematics, 22 (1967), pp. 1-8.
3. J. Diestel, A. M. Peralta and D. Puglisi, Sequential w-right continuity and summing operators, Math. Nachr., 284 (5–6) (2011), pp. 664–680.
4. A. Ghaffari and S. Javadi, ϕ-Connes amenability of dual Banach algebras, Bull. Iran. Math. Soc., 43 (2017), pp. 25-39.
5. A. Ghaffari, S. Javadi and E. Tamini, Connes amenability of l1-Munn algebras, Tamkang Journal of Mathematics, 53 (2022), pp. 259-266.
6. A. Ghaffari, T. Haddadi, S. Javadi and M. Sheibani, On the structure of hypergroups with respect to the induced topology, Rocky Mountain J. Math., 52 (2) (2022), pp. 519-533.
7. Z. Hu, M. S. Monfaredd and T. Traynor, On character amenable Banach algebras, Studia Math., 193 (1) (2009), pp. 53-78.
8. E. Kaniuth, A. T. Lau and J. Pym, On ϕ-amenability of Banach algebras, Math. Proc. Camb. Phil. Soc., 144 (2008), pp. 85-96.
9. G. Kothe, Topological Vector Spaces, Springer, 1969.
10. A. T. Lau and J. Pym, Concerning the second dual of the group algebra of a locally compact group, J. London Math. Soc., 2 (41) (1990), pp. 445-460.
11. A. M. Peralta, I. Villanueva, J. D. Maitland Wright and K. Ylinen, Topological characterisation of weakly compact operators, J. Math. Anal. Appl., 325 (2) (2007), pp. 968-974.
12. A. M. Peralta, I. Villanueva, J. D. Maitland Wright and K. Ylinen, Weakly compact operators and the strong∗ topology for a Banach space, Proc. R. Soc. Edinb. Section A Mathematics, 140 (6) (2010), pp. 1249-1267
13. A. M. Peralta, I. Villanueva, J. D. Maitland Wright and K. Ylinen, Quasi completely continuous multilinear operators, Proc. R. Soc. Edinb. Section A Mathematics, 140 (3) (2010), pp. 635-649.
14. J. Qiu, Local completeness and dual local quasi-completeness, Proc. Amer. Math. Soc., 129 (2000), pp. 1419-1425.
15. W. Rudin, Functional Analysis, McGraw Hill, New York, 1991.
16. V. Runde, Amenability for dual Banach algebras, Studia Math., 148 (2001), pp. 47-66.
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