Let M_{m,n} be the set of all m × n real matrices. A matrix A \in M_{m,n} is said to be row-dense if there are no zeros between two nonzero entries for every row of this matrix. We find the structure of linear functions T: M_{m,n} \rightarrow M_{m,n} that preserve or strongly preserve row-dense matrices, i.e., T(A) is row-dense whenever A is row-dense or T(A) is row-dense if and only if A is row-dense, respectively. Similarly, a matrix A \in M_{m,n} is called a column-dense matrix if every column of A is a column-dense vector. At the end, the structure of linear preservers (strong linear preservers) of column-dense matrices is found., Sara M. Motlaghian, Ali Armandnejad, Frank J. Hall., and Obsahuje seznam literatury
It is proved that a linear surjection $\Phi \:\mathcal A\rightarrow \mathcal B$, which preserves noninvertibility between semisimple, unital, complex Banach algebras, is automatically injective.