✦ LIBER ✦
Multiplicative maps preserving the higher rank numerical ranges and radii
✍ Scribed by Sean Clark; Chi-Kwong Li; Nung-Sing Sze
- Publisher
- Elsevier Science
- Year
- 2010
- Tongue
- English
- Weight
- 185 KB
- Volume
- 432
- Category
- Article
- ISSN
- 0024-3795
No coin nor oath required. For personal study only.
✦ Synopsis
Let M n be the semigroup of n × n complex matrices under the usual multiplication, and let S be different subgroups or semigroups in M n including the (special) unitary group, (special) general linear group, the semigroups of matrices with bounded ranks. Suppose Λ k (A) is the rank-k numerical range and r k (A) is the rank-k numerical radius of A ∈ M n . Multiplicative maps φ : S → M n satisfying r k (φ(A)) = r k (A) are characterized. From these results, one can deduce the structure of multiplicative preservers of Λ k (A).