The metrics of Hermitian holomorphic vector bundles and the similarity of Cowen-Douglas operators

被引:1
作者
Ji, Kui [1 ]
Ji, Shanshan [1 ]
机构
[1] Hebei Normal Univ, Dept Math Sci, Shijiazhuang 050016, Hebei, Peoples R China
基金
中国国家自然科学基金;
关键词
Cowen-Douglas operator; Similarity equivalence; Holomorphic vector bundle; CURVATURE;
D O I
10.1007/s13226-021-00168-8
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this note, we investigate the similarity of Cowen-Douglas operators with index one in terms of the ratio of metrics of the corresponding holomorphic bundles. For the case of index two, we give some sufficient and necessary conditions for the similarity of M-z* circle plus M-z* by using the ratio of determinants of the metrics, where M-z is the multiplication operator of weighted Bergman spaces.
引用
收藏
页码:736 / 749
页数:14
相关论文
共 11 条
  • [1] AGLER J, 1985, J OPERAT THEOR, V13, P203
  • [2] Agler J., 1982, Integ. Equ. Oper. Theory, V5, P608
  • [3] CLARK DN, 1983, MICH MATH J, V30, P361
  • [4] CLARK DN, 1985, J LOND MATH SOC, V31, P357
  • [5] COMPLEX GEOMETRY AND OPERATOR THEORY
    COWEN, MJ
    DOUGLAS, RG
    [J]. ACTA MATHEMATICA, 1978, 141 (3-4) : 187 - 261
  • [6] A subclass of the Cowen-Douglas class and similarity
    Ji, Kui
    Kwon, Hyun-Kyoung
    Sarkar, Jaydeb
    Xu, Jing
    [J]. MATHEMATISCHE NACHRICHTEN, 2022, 295 (11) : 2197 - 2222
  • [7] Rigidity of the flag structure for a class of Cowen-Douglas operators
    Ji, Kui
    Jiang, Chunlan
    Keshari, Dinesh Kumar
    Misra, Gadadhar
    [J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2017, 272 (07) : 2899 - 2932
  • [8] K-group and similarity classification of operators
    Jiang, CL
    Guo, XZ
    Ji, K
    [J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2005, 225 (01) : 167 - 192
  • [9] Shields A., 1974, TOPICS OPERATOR THEO, V13, P49
  • [10] Wang, 1998, HARLOW PITMAN RES NO