Maps preserving the inner local spectral radius zero of generalized product of operators

Jordan product and fixed points preservers

“…The study of maps on operators or matrices that leave some properties invariant, is the most active problems in the last decades, see for instance [1,3,5,6,8].…”

Maps preserving fixed points of generalized product of operators

“…The problem of characterizing maps on matrices or operators that preserve certain functions, subsets and relations has attracted the attention of many mathematicians in the last decade; for example we can see [1,2,3,4,5,6,7] and their references. In recent years, a great activity has occurred in characterising maps preserving the subspace of fixed points of a matrix or operators.…”