The star-shapedness of a generalized numerical range
| Autor: | Tuen-Wai Ng, Nam-Kiu Tsing, Pan-Shun Lau |
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| Rok vydání: | 2016 |
| Předmět: |
Numerical Analysis
Algebra and Number Theory Mathematics::Operator Algebras 010102 general mathematics Diagonalizable matrix Center (category theory) 010103 numerical & computational mathematics Star (graph theory) 01 natural sciences Hermitian matrix Functional Analysis (math.FA) Combinatorics Mathematics - Functional Analysis FOS: Mathematics 15A04 15A60 Discrete Mathematics and Combinatorics Geometry and Topology 0101 mathematics Numerical range Mathematics |
| DOI: | 10.48550/arxiv.1608.06094 |
| Popis: | Let H n be the set of all n × n Hermitian matrices and H n m be the set of all m-tuples of n × n Hermitian matrices. For A = ( A 1 , . . . , A m ) ∈ H n m and for any linear map L : H n m → R l , we define the L-numerical range of A by W L ( A ) : = { L ( U ⁎ A 1 U , . . . , U ⁎ A m U ) : U ∈ C n × n , U ⁎ U = I n } . In this paper, we prove that if l ≤ 3 , n ≥ l and A 1 , . . . , A m are simultaneously unitarily diagonalizable, then W L ( A ) is star-shaped with star center at L ( tr A 1 n I n , . . . , tr A m n I n ) . |
| Databáze: | OpenAIRE |
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