Acta mathematica scientia,Series A ›› 2012, Vol. 32 ›› Issue (1): 103-112.

• Articles • Previous Articles     Next Articles

On Rank Invariance of Generalized Block Pick Matrices of Matrix-valued Caratheodory Functions

 HE Qin1, XU Qing-Zhou2, CHEN Gong-Ning1,3   

  1. 1.School of Mathematical and Statistics, Xuchang University, Henan Xuchang 461000;
    2.School of International Education, Xuchang University, Henan Xuchang 461000;
    3.School of Mathematical Sciences, Beijing Normal University, Beijing 100875
  • Received:2010-08-15 Revised:2011-04-23 Online:2012-02-25 Published:2012-02-25
  • Supported by:

    国家自然科学基金(10701009)资助

Abstract:

Lasarow[1] derived statements on the rank invariance of generalized block Pick matrices of matrix-valued Carath′eodory functions. In this paper, it is concluded that the rank of such generalized block Pick matrices can be related to and coincides with the rank of some block Toeplitz matrices in terms of the Toeplitz vector approach given in [2]. These results are used to improve the proof of the rank invariance of the generalized block Pick matrices in certain sence.

Key words: Matrix-valued Caratheodory function, Generalized block Pick matrix, Block Toeplitz matrix, Rank invariance

CLC Number: 

  • 47A57
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