Pseudospectra of special operators and pseudospectrum preservers

Denote by B(H) the Banach algebra of all bounded linear operators on a complex Hilbert space H. Let A∈B(H), and denote by σ(A) the spectrum of A. For ε>0, define the ε-pseudospectrum σε(A) of A asσε(A)={z∈σ(A+E):E∈B(H),‖E‖<ε}. In this paper, the pseudospectra of several special classes of operators are characterized. As an application, complete descriptions are given of the maps of B(H) leaving invariant the pseudospectra of A
- B for different kinds of binary operations
- on operators such as the difference A−B, the operator product AB, and the Jordan product AB+BA.