On the Maximal and Minimal Left Ideals of Certain Banach Algebras on Locally Compact Groups
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- 作者：Saeid Maghsoudi (1)
Rasoul Nasr-Isfahani (2) - 关键词：Primary 43A15 ; 43A20 ; Secondary 46H05 ; Arens product ; locally compact group ; maximal ideal ; radical
- 刊名：Results in Mathematics
- 出版年：2012
- 出版时间：2 - September 2012
- 年：2012
- 卷：62
- 期：1
- 页码：157-165
- 全文大小：204KB
- 参考文献：1. Bahrami F., Nasr-Isfahani R., Soltani S.: Homological properties of certain Banach modules over group algebras. Proc. Edinburgh Math. Soc. 54, 321鈥?28 (2011) CrossRef
2. Civin P.: Ideals in the second conjugate algebra of a group algebra. Math. Scand. 11, 161鈥?74 (1962)
3. Civin P.: Annihilators in the second conjugate algebra of a group algebra. Pac. J. Math. 12, 855鈥?62 (1962)
4. Civin P., Yood B.: The second conjugate space of a Banach algebra as an algebra. Pac. J. Math. 11, 847鈥?70 (1961)
5. Dales H.G.: Banach Algebras and Automatic Continuity. Oxford University Press, New York (2000)
6. Filali M.: The ideal structure of some Banach algebras. Math. Proc. Cambridge Philos. Soc. 111, 567鈥?76 (1992) CrossRef
7. Filali, M., Sangani Monfared M.: Finite dimensional left ideals in the dual of introverted spaces. Proc. Amer. Math. Soc. (2011, in press)
8. Floret K.: Minimal ideals of / n-homogeneous polynomials on Banach spaces. Results. Math. 39, 201鈥?17 (2001)
9. Granirer E.: The radical of / L 鈭?/sup>( / G)*. Proc. Am. Math. Soc. 41, 321鈥?24 (1973)
10. Gulick S.: Commutativity and ideals in the biduals of topological algebras. Pac. J. Math. 18, 121鈥?37 (1966)
11. Hewitt E., Ross K.: Abstract Harmonic Analysis I. Springer, New York (1970)
12. I艧ik N., Pym J., A. 脺lger A. : The second dual of the group algebra of a compact group. J. Lond. Math. Soc. 35, 135鈥?(1987) CrossRef
13. Lau A.T., Pym J.: Concerning the second dual of the group algebra of a locally compact group. J. Lond. Math. Soc. 41, 445鈥?60 (1990) CrossRef
14. Lau A.T., 脺lger A.: Topological centers of certain dual algebras. Trans. Am. Math. Soc. 348, 1191鈥?(1996) CrossRef
15. Lau A.T., James C., Wong S.: Invariant subspaces for algebras of linear operators and amenable locally compact groups. Proc. Am. Math. Soc. 102, 581鈥?86 (1988) CrossRef
16. Maghsoudi S., Nasr-Isfahani R., Rejali A.: Strong Arens irregularity of Beurling algebras with a locally convex topology. Arch. Math. (Basel) 86, 437鈥?48 (2006) CrossRef
17. Mehdipour M.J., Nasr-Isfahani R.: Compact left multipliers on Banach algebras related to locally compact groups. Bull. Austral. Math. Soc. 79, 227鈥?38 (2009) CrossRef
18. Rickart C.E.: General Theory of Banach Algebras. D. van Nostrand, New York (1960)
19. Singh A.I.: ${L^\infty_0(G)^*}$ as the second dual of the group algebra / L 1( / G) with a locally convex topology. Mich. Math. J. 46, 143鈥?50 (1999) CrossRef - 作者单位：Saeid Maghsoudi (1)
Rasoul Nasr-Isfahani (2)
1. Department of Mathematics, Zanjan University, 313, Zanjan, Iran
2. Department of Mathematical Sciences, Isfahan University of Technology, 84156-83111, Isfahan, Iran - ISSN：1420-9012
文摘
Let ${L_0^\infty(G)}$ be the Banach space of all essentially bounded measurable functions on a locally compact group G vanishing at infinity. In this paper, we describe maximal and minimal left ideals in the Banach algebra ${L_0^\infty(G)^*}$ equipped with an Arens type product. We also investigate some spectral properties of ${L_0^\infty(G)^*}$ .