Two distance preservers of generalized numerical radii

Abstract

Let be a complex Hilbert space and let be the set of all bounded linear operators on . For every , the joint numerical radius of is denoted by . We give a description for surjective mappings such that for all , when is infinite-dimensional. This complements a recent result of Li and Poon for such mappings when is finite-dimensional. We also study the Davis–Wielandt radius, , of . A description for surjective mappings such that for all is also given.

Keywords:

• joint numerical range
• joint numerical radius
• Davis–Wielandt shell
• preserver

AMS Subject Classifications:

• 47A12
• 47B49