Transforms for Operators and Symplectic Automorphisms over a Locally Compact Abelian Group.
Two characterizations of automorphisms on B(X)
Let X be an infinite-dimensional Banach space, and let ϕ be a surjective linear map on B(X) with ϕ(I) = I. If ϕ preserves injective operators in both directions then ϕ is an automorphism of the algebra B(X). If X is a Hilbert space, then ϕ is an automorphism of B(X) if and only if it preserves surjective operators in both directions.
Weak essential spectra of multiplication operators on spaces of bounded linear operators.
Zero product preservers and orthogonality preservers on algebras of unbounded operators.