Analysis of Spectral Points of the Operators T[*]T and TT[*] in a Krein Space

被引:5
作者
Ran, Andre [1 ]
Wojtylak, Michal [1 ]
机构
[1] Vrije Univ Amsterdam, Fac Exact Sci, Dept Math, NL-1081 HV Amsterdam, Netherlands
关键词
Regular critical point; singular critical point; Jordan chain; Krein space; INDEFINITE SCALAR PRODUCT; POLAR DECOMPOSITIONS;
D O I
10.1007/s00020-009-1654-5
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Spectra and sets of regular and singular critical points of definitizable operators of the form (TT)-T-[*] and TT[*] in a Krein space are compared. The relation between the Jordan chains of the above operators (corresponding to the same eigenvalue) is shown.
引用
收藏
页码:263 / 280
页数:18
相关论文
共 19 条
[1]  
[Anonymous], 1982, MATH RES
[2]  
Bognar J., 1974, Indefinite Inner Product Spaces
[3]  
Bolshakov Y, 1997, LINEAR ALGEBRA APPL, V261, P91
[4]   UNITARY EQUIVALENCE IN AN INDEFINITE SCALAR PRODUCT - AN ANALOG OF SINGULAR-VALUE DECOMPOSITION [J].
BOLSHAKOV, Y ;
REICHSTEIN, B .
LINEAR ALGEBRA AND ITS APPLICATIONS, 1995, 222 :155-226
[5]   On singular critical points of positive operators in Krein spaces [J].
Curgus, B ;
Gheondea, A ;
Langer, H .
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2000, 128 (09) :2621-2626
[6]  
Dunford N., 1963, Linear Operators, V1st edition
[7]   ELEMENTARY DIVISORS OF AB AND BA [J].
FLANDERS, H .
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1951, 2 (06) :871-874
[8]  
Gohberg I., 2005, Indefinite Linear Algebra and Applications
[9]  
HALMOS P. R., 2012, HILBERT SPACE PROBLE, V19
[10]  
JONAS P, 1992, OPER THEORY ADV APPL, V59, P252