ArticleOriginal scientific text

Title

On isomorphisms of standard operator algebras

Authors 1

Affiliations

  1. Institute of Mathematics and Informatics, Faculty of Natural Sciences, University of Debrecen, P.O. Box 12, 4010 Debrecen, Hungary

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.

Bibliography

  1. M. Brešar, Jordan mappings of semiprime rings, J. Algebra 127 (1989), 218-228.
  2. M. Brešar and P. Šemrl, Mappings which preserve idempotents, local automorphisms, and local derivations, Canad. J. Math. 45 (1993), 483-496.
  3. J. Hakeda, Additivity of *-semigroup isomorphisms among *-algebras, Bull. London Math. Soc. 18 (1986), 51-56.
  4. I. N. Herstein, On a type of Jordan mappings, An. Acad. Bras. Cienc. 39 (1967), 357-360.
  5. I. N. Herstein, Topics in Ring Theory, Univ. of Chicago Press, Chicago, 1969.
  6. H. Kestelman, Automorphisms of the field of complex numbers, Proc. London Math. Soc. (2) 53 (1951), 1-12.
  7. W. S. Martindale III, When are multiplicative mappings additive? Proc. Amer. Math. Soc. 21 (1969), 695-698.
  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. M. Omladič and P. Šemrl, Linear mappings that preserve potent operators, Proc. Amer. Math. Soc. 123 (1995), 1069-1074.
  10. P. G. Ovchinnikov, Automorphisms of the poset of skew projections, J. Funct. Anal. 115 (1993), 184-189.
  11. P. Šemrl, Isomorphisms of standard operator algebras, Proc. Amer. Math. Soc. 123 (1995), 1851-1855.
Pages:
295-302
Main language of publication
English
Received
2000-02-28
Accepted
2000-05-04
Published
2000
Exact and natural sciences