Characterizing linear maps of standard operator algebras through orthogonality

Abstract

Let A be a standard operator algebra on a Hilbert space H with dimH ≥ 2, and A is closed under the adjoint operation. In this article, all linear maps δ; τ : A ! B(H) satisfying Aτ(B)∗ + δ(A)B∗ = 0 (A∗τ(B) + δ(A)∗B = 0) whenever AB∗ = 0 (A∗B = 0) are characterized, and as an application, linear maps on A behaving like right (left) centralizers at orthogonal elements are described