A note on equivalence preserving maps. Issue 11 (1st November 2020)

• Record Type: Journal Article
• Authors: Petek, Tatjana; Radić, Gordana
• Is Part Of: Linear & multilinear algebra. Volume 68:Issue 11(2020)
• Page Start: 2289
• Page End: 2297
• Publication Date: 2020-11-01
• Subjects: L. Molnar; Nonlinear maps -- equivalence -- equivalence preserving; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2019.1578727
• Languages: English
• ISSNs: 0308-1087

Abstract

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 ) .