Higher Dimensional Numerical Range of ξ-Lie Products on Bound Self-adjoint Operators.

Let H be a complex Hilbert space and B s (H) the Jordan algebra of all bounded self-adjoint linear operators on H. Assume that k is any positive integer with k < dim H and ξ is any complex number. In this paper, we first give some useful properties about k-dimensional numerical range of ξ -Lie product [ A , B ] ξ = A B - ξ B A for A , B ∈ B s (H) ; and then, based on these properties, all surjective maps preserving k-dimensional numerical ranges of ξ -Lie product on B s (H) are completely characterized. [ABSTRACT FROM AUTHOR]