Acta mathematica scientia,Series B ›› 2003, Vol. 23 ›› Issue (2): 192-.

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CO-ISOMETRIC SOLUTIONS OF EQUATIONCU + U*C = 2D

 DU Quan-Beng, HOU Jin-Chuan   

  1. Department of Mathematics, Shanxi University, Taiyuan 030000, China
    Department of Mathematics, Shanxi Teachers University, Linfen 041004, China
    Department of Mathematics, Shanxi Teachers University, Linfen 041004, China
  • Online:2003-04-07 Published:2003-04-07
  • Supported by:

    Received February 26, 2001. This work is supported by NNSFC and PNSFS

Abstract:

This note discusses the co-isometric solutions of the operator equation CU +
U*C = 2D, establishes a correspondence between such solutions and the self-adjoint so-
lutions of the algebraic Riccati equation X^2− iDX + iXD + D^2− C^2 = 0, and gives all
possible co-isometric solutions parametrically. Some mistakes of Dobovivsek’s results are
corrected.

Key words: s Co-isometric operator, invariant subspace, factorization

CLC Number: 

  • 15A24
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