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A matrix completion problem has been exploited amply because of its abundant applications and the analysis of contractions enables us to have insight into structure and space of operators. In this article, we focus on a specific completion problem related to Hankel partial contractions. We provide concrete necessary and sufficient conditions for the existence of completion of Hankel partial contractions for both extremal and non-extremal types with lower dimensional matrices. Moreover, we give a negative answer for the conjecture presented in [8]. For our results, we use several tools such as the Nested Determinants Test (or Choleski’s Algorithm), the Moore-Penrose inverse, the Schur product techniques, and a congruence of two positive semi-definite matrices; all these suggest an algorithmic approach to solve the contractive completion problem for general Hankel matrices of size n × n in both types.
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참고문헌 (26)
참고문헌 신청
C. Davis / 1976 / An extremal problem for extensions of a sesquilinear form / Linear Algebra Appl 13 (1-2) : 91 ~ 102
C. Davis / 1982 / Norm-preserving dilations and their application to optimal error bounds / SIAM J. Numer. Anal 19 (3) : 445 ~ 469
C. Foia¸s / 1984 / Redheffer products and the lifting of contractions on Hilbert space / J. Operator Theory 11 (1) : 193 ~ 196
C. R. Johnson / 1986 / Completion of partial matrices to contractions / J. Funct. Anal 69 (2) : 260 ~ 267
C. R. Johnson / 1988 / Completion of Toeplitz partial contractions / SIAM J. Matrix Anal. Appl 9 (2) : 159 ~ 167
C. Davis / 1982 / Norm-preserving dilations and their application to optimal error bounds / SIAM J. Numer. Anal 19 (3) : 445 ~ 469
C. Foia¸s / 1984 / Redheffer products and the lifting of contractions on Hilbert space / J. Operator Theory 11 (1) : 193 ~ 196
C. R. Johnson / 1986 / Completion of partial matrices to contractions / J. Funct. Anal 69 (2) : 260 ~ 267
C. R. Johnson / 1988 / Completion of Toeplitz partial contractions / SIAM J. Matrix Anal. Appl 9 (2) : 159 ~ 167
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