We show that between standard operator algebras every bijective map with a certain multiplicativity property related to Jordan triple isomorphisms of associative rings is automatically additive.
@article{bwmeta1.element.bwnjournal-article-smv142i3p295bwm, author = {Lajos Moln\'ar}, title = {On isomorphisms of standard operator algebras}, journal = {Studia Mathematica}, volume = {141}, year = {2000}, pages = {295-302}, zbl = {1049.47503}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv142i3p295bwm} }
Molnár, Lajos. On isomorphisms of standard operator algebras. Studia Mathematica, Tome 141 (2000) pp. 295-302. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv142i3p295bwm/
[000] [1] M. Brešar, Jordan mappings of semiprime rings, J. Algebra 127 (1989), 218-228. | Zbl 0691.16040
[001] [2] M. Brešar and P. Šemrl, Mappings which preserve idempotents, local automorphisms, and local derivations, Canad. J. Math. 45 (1993), 483-496. | Zbl 0796.15001
[002] [3] J. Hakeda, Additivity of *-semigroup isomorphisms among *-algebras, Bull. London Math. Soc. 18 (1986), 51-56. | Zbl 0557.46037
[003] [4] I. N. Herstein, On a type of Jordan mappings, An. Acad. Bras. Cienc. 39 (1967), 357-360. | Zbl 0199.07503
[004] [5] I. N. Herstein, Topics in Ring Theory, Univ. of Chicago Press, Chicago, 1969. | Zbl 0232.16001
[005] [6] H. Kestelman, Automorphisms of the field of complex numbers, Proc. London Math. Soc. (2) 53 (1951), 1-12. | Zbl 0042.39304
[006] [7] W. S. Martindale III, When are multiplicative mappings additive? Proc. Amer. Math. Soc. 21 (1969), 695-698. | Zbl 0175.02902
[007] [8] L. Molnár, *-semigroup endomorphisms of B(H), in: I. Gohberg (ed.), Proc. Memorial Conference for Béla Szőkefalvi-Nagy, Szeged, 1999, Oper. Theory Adv. Appl. (to appear).
[008] [9] M. Omladič and P. Šemrl, Linear mappings that preserve potent operators, Proc. Amer. Math. Soc. 123 (1995), 1069-1074. | Zbl 0831.47026
[009] [10] P. G. Ovchinnikov, Automorphisms of the poset of skew projections, J. Funct. Anal. 115 (1993), 184-189. | Zbl 0806.46069
[010] [11] P. Šemrl, Isomorphisms of standard operator algebras, Proc. Amer. Math. Soc. 123 (1995), 1851-1855. | Zbl 0824.47037