On isomorphisms of standard operator algebras

Lajos Molnár

Studia Mathematica (2000)

  • Volume: 142, Issue: 3, page 295-302
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Molnár, Lajos. "On isomorphisms of standard operator algebras." Studia Mathematica 142.3 (2000): 295-302. <http://eudml.org/doc/216805>.

@article{Molnár2000,
abstract = {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.},
author = {Molnár, Lajos},
journal = {Studia Mathematica},
keywords = {operator algebras; Jordan triple isomorphisms; automatically additive},
language = {eng},
number = {3},
pages = {295-302},
title = {On isomorphisms of standard operator algebras},
url = {http://eudml.org/doc/216805},
volume = {142},
year = {2000},
}

TY - JOUR
AU - Molnár, Lajos
TI - On isomorphisms of standard operator algebras
JO - Studia Mathematica
PY - 2000
VL - 142
IS - 3
SP - 295
EP - 302
AB - 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.
LA - eng
KW - operator algebras; Jordan triple isomorphisms; automatically additive
UR - http://eudml.org/doc/216805
ER -

References

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  1. [1] M. Brešar, Jordan mappings of semiprime rings, J. Algebra 127 (1989), 218-228. Zbl0691.16040
  2. [2] M. Brešar and P. Šemrl, Mappings which preserve idempotents, local automorphisms, and local derivations, Canad. J. Math. 45 (1993), 483-496. Zbl0796.15001
  3. [3] J. Hakeda, Additivity of *-semigroup isomorphisms among *-algebras, Bull. London Math. Soc. 18 (1986), 51-56. Zbl0557.46037
  4. [4] I. N. Herstein, On a type of Jordan mappings, An. Acad. Bras. Cienc. 39 (1967), 357-360. Zbl0199.07503
  5. [5] I. N. Herstein, Topics in Ring Theory, Univ. of Chicago Press, Chicago, 1969. Zbl0232.16001
  6. [6] H. Kestelman, Automorphisms of the field of complex numbers, Proc. London Math. Soc. (2) 53 (1951), 1-12. Zbl0042.39304
  7. [7] W. S. Martindale III, When are multiplicative mappings additive? Proc. Amer. Math. Soc. 21 (1969), 695-698. Zbl0175.02902
  8. [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). 
  9. [9] M. Omladič and P. Šemrl, Linear mappings that preserve potent operators, Proc. Amer. Math. Soc. 123 (1995), 1069-1074. Zbl0831.47026
  10. [10] P. G. Ovchinnikov, Automorphisms of the poset of skew projections, J. Funct. Anal. 115 (1993), 184-189. Zbl0806.46069
  11. [11] P. Šemrl, Isomorphisms of standard operator algebras, Proc. Amer. Math. Soc. 123 (1995), 1851-1855. Zbl0824.47037

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