On the hyperbolicity of the Krein space numerical range

被引：0
作者：
Bebiano, N. [1 ]
Lemos, R. [2 ]
Soares, G. [3 ]
机构：
[1] Univ Coimbra, Math Dept, CMUC, Coimbra, Portugal
[2] Univ Aveiro, Math Dept, CIDMA, Aveiro, Portugal
[3] Univ Tras Os Montes & Alto Douro, CMAT UTAD, Vila Real, Portugal
来源：
LINEAR & MULTILINEAR ALGEBRA | 2024年 / 72卷 / 14期
关键词：
Indefinite numerical range; classical numerical range; J-Hermitian matrix; hyperbolical range theorem; OPERATORS;
D O I：
10.1080/03081087.2023.2251648
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper a necessary and sufficient condition for hyperbolicity of the indefinite numerical range is established. As a consequence, an indefinite version of Brown-Spitkovsky theorem stating the ellipticity of the numerical range of certain tridiagonal matrices is revisited. This result leads to necessary and sufficient conditions for hyperbolicity of indefinite numerical ranges of new classes of tridiagonal matrices.
引用
收藏
页码：2267 / 2287
页数：21
相关论文
共 14 条
  • [1] Bebiano N, 2008, ELECTRON J LINEAR AL, V17
  • [2] On the geometry of numerical ranges in spaces with an indefinite inner product
    Bebiano, N
    Lemos, R
    da Providência, J
    Soares, G
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2005, 399 : 17 - 34
  • [3] On generalized numerical ranges of operators on an indefinite inner product space
    Bebiano, N
    Lemos, R
    da Providência, J
    Soares, G
    [J]. LINEAR & MULTILINEAR ALGEBRA, 2004, 52 (3-4) : 203 - 233
  • [4] Kippenhahn Curves of Some Tridiagonal Matrices
    Bebiano, Natalia
    da Providencia, Joao
    Spitkovsky, Ilya
    Vazquez, Kenya
    [J]. FILOMAT, 2021, 35 (09) : 3047 - 3061
  • [5] On matrices with elliptical numerical ranges
    Brown, ES
    Spitkovsky, IM
    [J]. LINEAR & MULTILINEAR ALGEBRA, 2004, 52 (3-4) : 177 - 193
  • [6] On geometric properties of the numerical range
    Chien, MT
    Yeh, L
    Yeh, YT
    Lin, FZ
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1998, 274 : 389 - 410
  • [7] On the numerical range of some block matrices with scalar diagonal blocks
    Geryba, Titas
    Spitkovsky, Ilya M.
    [J]. LINEAR & MULTILINEAR ALGEBRA, 2021, 69 (05) : 772 - 785
  • [8] Gohberg I., 1983, Operator Theory: Advances and Applications, V8
  • [9] The standard value of a bilinear form.
    Hausdorff, F
    [J]. MATHEMATISCHE ZEITSCHRIFT, 1919, 3 : 314 - 316
  • [10] Li C-K., 1998, Electron. J. Linear Algebra, V3, P31, DOI [10.13001/1081-3810.1013, DOI 10.13001/1081-3810.1013]
12