A Characterization of Jacobson Radical in Γ-Banach Algebras

ABSTRACT

Let*V*_{1} and *V*_{2} be two -Banach algebras and *R*_{i} be the right operator Banach algebra and *L*_{i} be the left operator Banach algebra of V_{i}(i=1,2). We give a characterization of the Jacobson radical for the projective tensor product *V*_{1}_{r}V_{2} in terms of the Jacobson radical for R_{1}_{r}L_{2}. If *V*_{1} and *V*_{2} are isomorphic, then we show that this characterization can also be given in terms of the Jacobson radical for *R*_{2}_{r}L_{1}.

Let

Cite this paper

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.

N. Goswami, "A Characterization of Jacobson Radical in Γ-Banach Algebras,"

References

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[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.

[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.