Additive mappings preserving operators of rank one

Additive Preserving Rank One Maps on Hilbert C-modules

In this paper, we characterize a class of additive maps on Hilbert C∗-modules which maps a ”rank one” adjointable operators to another rank one operators.

Additive Maps Preserving Idempotency of Products or Jordan Products of Operators

Let $mathcal{H}$ and $mathcal{K}$ be infinite dimensional Hilbert spaces, while $mathcal{B(H)}$ and $mathcal{B(K)}$ denote the algebras of all linear bounded operators on $mathcal{H}$ and $mathcal{K}$, respectively. We characterize the forms of additive mappings from $mathcal{B(H)}$ into $mathcal{B(K)}$ that preserve the nonzero idempotency of either Jordan products of operators or usual produc...

Rank one perturbations of self-adjoint operators

A characterization of orthogonality preserving operators

‎In this paper‎, ‎we characterize the class of orthogonality preserving operators on an infinite-dimensional Hilbert space $H$ as scalar multiples of unitary operators between $H$ and some closed subspaces of $H$‎. ‎We show that any circle (centered at the origin) is the spectrum of an orthogonality preserving operator‎. ‎Also‎, ‎we prove that every compact normal operator is a strongly orthogo...

Operators with Singular Continuous Spectrum: Ii. Rank One Operators

For an operator, A, with cyclic vector φ, we study A+ λP where P is the rank one projection onto multiples of φ. If [α,β] ⊂ spec(A) and A has no a.c. spectrum, we prove that A + λP has purely singular continuous spectrum on (α, β) for a dense Gδ of λ’s. §