On maps preserving square-zero matrices

Maps on upper triangular matrices preserving zero products

“…Such matrices were also investigated in [12], where the linear maps preserving square-zero matrices were studied. This was extended in [6] to the matrices over commutative rings. Quite a lot of authors studied zero product preservers on Banach algebras, see [1], [5], but also on some Hilbert spaces, see [9], or topological spaces, see [7].…”

Preserving Zeros of a Polynomial

“…Bijective linear operators on the matrix algebra preserving zeros of the involutory polynomial p(x, y) = xy − yx * are classified in [14]. Additive surjections on certain classes of algebras, preserving zeros of p(x) = x 2 or preserving zeros of the Jordan polynomial p(x, y) = xy + yx, were characterized in [15,Theorem 4.1], [26,Lemma 2.3], and in [38].…”

On Maps Preserving Zero Jordan Products

“…Actually, the only related paper we were aware of is the one by S Semrl [28] which deals with maps preserving square-zero matrices of sl n , the set of n  n complex matrices with trace zero. Recently, we described maps preserving zero Jordan products on the Jordan algebra of all Hermitian operators [17] and maps preserving square-zero matrices over unital commutative rings [16].…”