A note on equivalence preserving maps. Issue 11 (1st November 2020) - Petek, Tatjana; Radić, Gordana
ABSTRACT: Let B ( X ) be the algebra of all bounded linear operators on complex Banach space X and let the relation A ∼ B, A, B ∈ B ( X ), denote B = TAS for some invertible T, S ∈ B ( X ) . We will give a complete description of surjective maps on B ( X ) such that A − B ∼ C if and only if φ A − φ B ∼ φ C, for every A, B, C ∈ B ( X ) .