Involution similarity preserving linear maps
Tom 249 / 2019
Studia Mathematica 249 (2019), 319-328
MSC: Primary 47B49.
DOI: 10.4064/sm180311-5-7
Opublikowany online: 23 April 2019
Streszczenie
Let be a Banach space with dimension at least 3. Two operators A and B in B(X) are said to be p-similar if there is a product S of finitely many involutions such that A=SBS^{-1}. In this paper, we investigate linear bijections \Phi : B(X) \to B(X) such that \Phi (A) and \Phi (B) are similar whenever A and B are p-similar. We show that such a map is either an isomorphism or an anti-isomorphism plus a p-similarity invariant functional. This result can be used to characterize Lie isomorphisms and Jordan isomorphisms.
