چكيده فارسي :
In recent years, there has been a considerable attention to non-linear mappings on algebras
of operators that preserve certain properties of operators. For examples of such maps we can
refer to non-linear maps that preserve the invertibility, the spectrum or the other properties of
each operator. In this note, we refer to some recent results concerning maps between algebras of
operators on Banach spaces preserving any of the surjectivity, the injectivity, and the boundedness
from below of the difference and sum of operators. More precisely, for infinite dimensional Banach
spaces X and Y we consider maps from $B(X)$ onto $B(Y )$ satisfying
$$c(\phi(S)\pm \phi(T))=c(S\pm T)$$
for all $S,T\in B(X)$, where $c(.)$ stands either for the minimum modulus, or the surjectivity
modulus, or the maximum modulus. We also refer to some known results for the finite dimensional
case on maps preserving the minimum modulus of the difference of matrices.
