Polar decompositions of normal operators in indefinite inner product spaces

被引：11
|
作者：
Mehl, Christian
Ran, Andre C. M.
Rodman, Leiba
机构：
[1] Tech Univ Berlin, Inst Math, D-10623 Berlin, Germany
[2] Free Univ Amsterdam, Fac Exacte Wetenshcappen, NL-1081 HV Amsterdam, Netherlands
[3] Coll William & Mary, Dept Math, Williamsburg, VA 23187 USA
来源：
OPERATOR THEORY IN KREIN SPACES AND NONLINEAR EIGENVALUE PROBLEMS | 2006年 / 162卷
关键词：
Krein spaces; polar decompositions; normal operators; indefinite inner products;
D O I：
10.1007/3-7643-7453-5_15
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Polar decompositions of normal matrices in indefinite inner product spaces are studied. The main result of this paper provides sufficient conditions for a normal operator in a Krein space to admit a polar decomposition. As an application of this result, we show that any normal matrix in a finite-dimensional indefinite inner product space admits a polar decomposition which answers affirmatively an open question formulated in [2]. Furthermore, necessary and sufficient conditions are given for a matrix to admit a polar decomposition and for a normal matrix to admit a polar decomposition with commuting factors.
引用
收藏
页码：277 / 292
页数：16
相关论文
共 50 条
  • [1] POLAR DECOMPOSITIONS OF QUATERNION MATRICES IN INDEFINITE INNER PRODUCT SPACES
    Groenewald, Gilbert J.
    Van Rensburg, Dawie B. Janse
    Ran, Andre C. M.
    Theron, Frieda
    Van Straaten, Madelein
    [J]. ELECTRONIC JOURNAL OF LINEAR ALGEBRA, 2021, 37 : 659 - 670
  • [2] Normal matrices and polar decompositions in indefinite inner products
    Lins, B
    Meade, P
    Mehl, C
    Rodman, L
    [J]. LINEAR & MULTILINEAR ALGEBRA, 2001, 49 (01): : 45 - 89
  • [3] Locally definite operators in indefinite inner product spaces
    H. Langer
    A. Markus
    V. Matsaev
    [J]. Mathematische Annalen, 1997, 308 : 405 - 424
  • [4] Extensions of Laguerre operators in indefinite inner product spaces
    Derkach, VA
    [J]. MATHEMATICAL NOTES, 1998, 63 (3-4) : 449 - 459
  • [5] Locally definite operators in indefinite inner product spaces
    Langer, H
    Markus, A
    Matsaev, V
    [J]. MATHEMATISCHE ANNALEN, 1997, 308 (03) : 405 - 424
  • [6] Extensions of Laguerre operators in indefinite inner product spaces
    V. A. Derkach
    [J]. Mathematical Notes, 1998, 63 : 449 - 459
  • [7] Factorizations into normal matrices in indefinite inner product spaces
    Sui, Xuefang
    Gondolo, Paolo
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2017, 516 : 143 - 166
  • [8] On classification of normal matrices in indefinite inner product spaces
    Mehl, C
    [J]. ELECTRONIC JOURNAL OF LINEAR ALGEBRA, 2006, 15 : 50 - 83
  • [9] Normal matrices in degenerate indefinite inner product spaces
    Mehl, Christian
    Trunk, Carsten
    [J]. OPERATOR THEORY IN INNER PRODUCT SPACES, 2007, 175 : 193 - 209
  • [10] OPERATORS OF FORM C]C IN INDEFINITE INNER PRODUCT SPACES
    BOGNAR, J
    KRAMLI, A
    [J]. ACTA SCIENTIARUM MATHEMATICARUM, 1968, 29 (1-2): : 19 - &
12345