Non-linear maps on self-adjoint operators preserving numerical radius and numerical range of Lie product

Abstract

Let be a complex separable Hilbert space of dimension , be the space of all self-adjoint operators on . We give a complete classification of non-linear surjective maps on preserving, respectively, numerical radius and numerical range of Lie product.

Keywords:

• numerical range
• numerical radius
• Lie product of operators
• general preservers

AMS Subject Classifications:

• 47H20
• 47B49
• 47A12

Additional information

Funding

This work was supported by National Science Foundation of China [grant number 11171249], [grant number 11201329], [grant number 11271217] and Program for the Outstanding Innovative Teams of Higher Learning Institutions of Shanxi.