A Characterization of Jacobson Radical in Γ-Banach Algebras


Let V1 and V2 be two -Banach algebras and Ri be the right operator Banach algebra and Li be the left operator Banach algebra of Vi(i=1,2). We give a characterization of the Jacobson radical for the projective tensor product V1rV2 in terms of the Jacobson radical for R1rL2. If V1 and V2 are isomorphic, then we show that this characterization can also be given in terms of the Jacobson radical for R2rL1.

Share and Cite:

N. Goswami, "A Characterization of Jacobson Radical in Γ-Banach Algebras," Advances in Pure Mathematics, Vol. 2 No. 6, 2012, pp. 413-418. doi: 10.4236/apm.2012.26062.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] S. Kyuno, “Notes on Jacobson Radicals of Gamma Rings,” Mathematica Japonica, Vol. 27, No. 1, 1982, pp. 107-111.
[2] W. E. Coppage and J. Luh, “Radicals of Gamma Rings,” Journal of the Mathematical Society of Japan, Vol. 23, No. 1, 1971, pp. 40-52. doi:10.2969/jmsj/02310040
[3] A. C. Paul and A. K. Azad, “Jacobson Radical for Gamma Rings,” Rajshahi University Studies Part-B. Journal of Science, Vol. 25, 1977, pp. 153-161.
[4] A. C. Paul and Md. S. Uddin, “On Jacobson Radical for Gamma Rings,” Ganit: Journal of Bangladesh Mathematical Society, Vol. 29, 2009, pp. 147-160.
[5] K. N. Raghavan, “The Jacobson Density Theorem and Applications,” 2005. http://www.imsc.res.in
[6] H. K. Nath, “A Study of Gamma-Banach Algebras,” Ph.D. Thesis, Gauhati University, Guwahati, 2001.
[7] W. E. Barnes, “On the ?-Rings of Nobusawa,” Pacific Journal of Mathematics, Vol. 18, No. 3, 1966, pp. 411-422.
[8] D. K. Bhattacharya and A. K. Maity, “Semilinear Tensor Product of ?-Banach Algebras,” Ganita, Vol. 40, No. 2, 1989, pp. 75-80.
[9] F. F. Bonsall and J. Duncan, “Complete Normed Algebras,” Springer-Verlag, Berlin, 1973. doi:10.1007/978-3-642-65669-9
[10] G. L. Booth, “Operator Rings of a ?-ring,” Math Japonica, Vol. 31, No. 2, 1986, pp. 175-183.
[11] N. J. Divinsky, “Rings and Radicals,” George Allen and Unwin, London, 1965.
[12] N. Goswami, “Some Results on Operator Banach Algebras of a ?-Banach Algebra,” Journal of Assam Academy of Mathematics, Vol. 1, 2010, pp. 40-48.
[13] N. Goswami, “On Levitzkinil Radical of Gamma Banach Algebras”, Global Journal of Applied Mathematics and Mathematical Sciences, 2012, in press.

Copyright © 2023 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.