Nonlinear maps preserving the minimum and surjectivity moduli

Abdellatif Bourhim, Javad Mashreghi, Anush Stepanyan

Abstract: Let X and Y be infinite-dimensional complex Banach spaces, and let B(X) (resp. B(Y)) denote the algebra of all bounded linear operators on X (resp. on Y). We describe maps φ from B(X) onto B(Y) satisfying c(φ(S)±φ(T))=c(S±T) for all S,T∈B(X), where c(⋅) stands either for the minimum modulus, or the surjectivity modulus, or the maximum modulus. We also obtain analog results for the finite-dimensional case.

Journal: Linear Algebra and its Applications. Volume 463 (2014), 171–189

DOI: 10.1016/j.laa.2014.09.002