Isometries of a generalized numerical radius
| Autor: | Maria Inez Cardoso Gonçalves, A. R. Sourour |
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| Rok vydání: | 2008 |
| Předmět: |
Normed algebra
Numerical Analysis Complex matrix Algebra and Number Theory 010102 general mathematics Mathematical analysis Hausdorff space Isometry 010103 numerical & computational mathematics Radius Generalized numerical range 01 natural sciences Combinatorics Metric space Discrete Mathematics and Combinatorics Geometry and Topology Generalized numerical radius 0101 mathematics Numerical range Mathematics Normed vector space |
| Zdroj: | Linear Algebra and its Applications. 429(7):1478-1488 |
| ISSN: | 0024-3795 |
| DOI: | 10.1016/j.laa.2008.04.007 |
| Popis: | For 0 q 1 , the q -numerical range is defined on the algebra M n of all n × n complex matrices by W q ( A ) = { x ∗ Ay : x , y ∈ C n , ∥ x ∥ = ∥ y ∥ = 1 , 〈 y , x 〉 = q } . The q -numerical radius is defined by r q ( A ) = max { | μ | : μ ∈ W q ( A ) } . We characterize isometries of the metric space ( M n , r q ) , i.e., the maps φ : M n → M n that satisfy r q ( A - B ) = r q ( φ ( A ) - φ ( B ) ) . We also characterize maps on M n that preserves the q -numerical range. The maps are not assumed to be linear. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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