Recent trends in the field of Jordan-Banach algebras

 Access to full text

 Full (PDF)

1. [1] A. A. Albert, On Jordan algebras of linear transformations, Trans. Amer. Math. Soc. 59 (1946), 524-555. Zbl0061.05101
2. [2] A. A. Albert, A structure theory for Jordan algebras, Ann. of Math. 48 (1947), 446-467. 
3. [3] B. Aupetit, Propriétés spectrales des algèbres de Banach, Lecture Notes in Math. 735, Springer, Heidelberg, 1979. Zbl0409.46054
4. [4] B. Aupetit, The uniqueness of the complete norm topology in Banach algebras and Banach-Jordan algebras, J. Funct. Anal. 47 (1982), 1-6. Zbl0488.46043
5. [5] B. Aupetit, Inessential elements in Banach algebras, Bull. London Math. Soc. 18 (1986), 493-497. Zbl0574.47015
6. [6] B. Aupetit, A Primer on Spectral Theory, Universitext, Springer, New York, 1991. 
7. [7] B. Aupetit, Spectral characterization of the radical in Banach and Jordan-Banach algebras, Math. Proc. Cambridge Philos. Soc. 114 (1993), 31-35. Zbl0811.46051
8. [8] B. Aupetit, Spectral characterization of the socle in Jordan-Banach algebras, to appear. 
9. [9] B. Aupetit et L. Baribeau, Sur le socle dans les algèbres de Jordan-Banach, Canad. J. Math. 41 (1989), 1090-1100. 
10. [10] B. Aupetit and H. du T. Mouton, Spectrum-preserving linear mappings in Banach algebras, Studia Math. 109 (1994), 91-100. Zbl0829.46039
11. [11] B. Aupetit and M. A. Youngson, On symmetry of Banach-Jordan algebras, Proc. Amer. Math. Soc. 91 (1984), 364-366. Zbl0526.46048
12. [12] B. Aupetit et A. Zraïbi, Propriétés analytiques du spectre dans les algèbres de Jordan-Banach, Manuscripta Math. 38 (1982), 381-386. Zbl0499.46030
13. [13] M. Benslimane, A. Fernández López et A. Kaïdi, Caractérisation des algèbres de Jordan-Banach de capacité finie, Bull. Sci. Math. (2) 112 (1988), 473-480. Zbl0679.46035
14. [14] M. Benslimane, O. Jaa and A. Kaïdi, The socle and the largest spectrum finite ideal, Quart. J. Math. Oxford (2) 42 (1991), 1-7. Zbl0722.17001
15. [15] M. Benslimane et A. Kaïdi, Structure des algèbres de Jordan-Banach non commutatives complexes régulières ou semi-simples à spectre fini, J. Algebra 113 (1988), 201-206. Zbl0692.46044
16. [16] M. Benslimane et A. Rodríguez Palacios, Caractérisation spectrale des algèbres de Jordan-Banach non commutatives complexes modulaires annihilatrices, J. Algebra 140 (1991), 344-354. Zbl0742.17002
17. [17] A. Fernández López, Modular annihilator Jordan algebras, Comm. Algebra 13 (1985), 2597-2613. Zbl0613.17015
18. [18] A. Fernández López, Noncommutative Jordan Riesz algebras, Quart. J. Math. Oxford (2) 39 (1988), 67-80. 
19. [19] A. Fernández López and A. Rodríguez Palacios, On the socle of a noncommutative Jordan algebra, Manuscripta Math. 56 (1986), 269-278. Zbl0598.17001
20. [20] A. Fernández López and A. Rodríguez Palacios, Primitive noncommutative Jordan algebras with nonzero socle, Proc. Amer. Math. Soc. 96 (1986), 199-206. Zbl0585.17001
21. [21] H. Hanche-Olsen and E. Størmer, Jordan Operator Algebras, Pitman, New York, 1984. 
22. [22] N. Jacobson, Structure and Representations of Jordan Algebras, Amer. Math. Soc. Colloq. Publ. 39, Amer. Math. Soc., Providence, R.I., 1968. 
23. [23] N. Jacobson, Lectures on Quadratic Jordan Algebras, Tata Institute of Fundamental Research, Bombay, 1969. 
24. [24] P. Jordan, J. von Neumann and E. Wigner, On an algebraic generalization of the quantum mechanical formalism, Ann. of Math. 35 (1934), 29-64. Zbl60.0902.02
25. [25] O. Loos, Properly algebraic and spectrum-finite ideals in Jordan systems, Math. Proc. Cambridge Philos. Soc. 114 (1993), 149-161. Zbl0786.17019
26. [26] J. Martínez Moreno, Sobre álgebras de Jordan normadas completas, Tesis doctoral, Universidad de Granada, 1977. 
27. [27] K. McCrimmon, The radical of a Jordan algebra, Proc. Nat. Acad. Sci. U.S.A. 62 (1969), 671-678. Zbl0175.31002
28. [28] K. McCrimmon, A characterization of the radical of a Jordan algebra, J. Algebra 18 (1971), 103-111. Zbl0243.17013
29. [29] J. M. Osborn, Representations and radicals of Jordan algebras, Scripta Math. 29 (1973), 297-329. Zbl0264.17006
30. [30] J. M. Osborn and M. L. Racine, Jordan rings with nonzero socle, Trans. Amer. Math. Soc. 251 (1979), 375-387. Zbl0409.17014
31. [31] P. S. Putter and B. Yood, Banach-Jordan *-algebras, Proc. London Math. Soc. (3) 41 (1980), 21-44. 
32. [32] A. Rodríguez Palacios, Jordan structures in analysis, preprint. 
33. [33] W. Sierpiński, Cardinal and Ordinal Numbers, PWN, Warszawa, 1958. 
34. [34] K. A. Zhevlakov, M., Slin'ko, J. P. Shestakov, and A. I. Shirshov, Rings That Are Nearly Associative, Academic Press, New York, 1982.