For 0 < |q| < 1, the q-numerical range is defined on the algebra Mn of all n x n complex matrices by
Wq(A) ={x*Ay : x, y Є Cn , x*x = y*y = 1, x* y = q}.
The q-numerical radius is defined by rq(A) = max{|μ| : μ Є Wq(A)}. We characterize
isometries of the metric space (Mn , rq) i.e., the maps φ : Mn → Mn that satisfy
rq(A - B) = rq(φ(A) - φ(B)). We also characterise maps on Mn that preserve the q-numerical range.
| Identifer | oai:union.ndltd.org:uvic.ca/oai:dspace.library.uvic.ca:1828/956 |
| Date | 22 May 2008 |
| Creators | Gonçalves, Maria Inez Cardoso |
| Contributors | Sourour, Ahmed Ramzi |
| Source Sets | University of Victoria |
| Language | English, English |
| Detected Language | English |
| Type | Thesis |
| Rights | Available to the World Wide Web |
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