Maps preserving equivalence by products of involutions
Gordana Radić · Operators and Matrices · 2019
Let B (X ) be the algebra of bounded linear operators on a complex Banach space X . Two operators A and B B (X ) are said to be equivalent by products of involutions, if A = T BS for T and S being a products of finitely many involutions. We will give description of linear bijective maps on B (X ) satisfying that (A) and (B) are equivalent (i.e. A = T BS for some invertible T,S B (X ) ) whenever A and B are equivalent by products of involutions.