Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
권호 표지
DOI QR코드

DOI QR Code

COMPLETION OF STOCHASTIC HANKEL PARTIAL CONTRACTIONS OF EXTREMAL TYPE

  • Lee, Jun Ik (Department of Mathematics Education Sangmyung University)
  • Received : 2011.07.06
  • Accepted : 2011.08.25
  • Published : 2011.09.30
Download PDF
⟨ Previous Next ⟩

Abstract

We find concrete necessary and sufficient conditions for the existence of contractive completions of Stochastic Hankel partial contractions of size $4{\times}4$, extremal type.

Keywords

References

  1. G. Arsene and A. Gheondea, Completing matrix contractions, J. Operator Th. 7 (1982), 179-189.
  2. W. Arveson, Interpolation problems in nest algebra, J. Funct. Anal. 20 (1975), 208-233. https://doi.org/10.1016/0022-1236(75)90041-5
  3. M. G. Crandall, Norm preserving extensions of linear transformations on Hilbert space, Proc. Amer. Math. Soc. 21 (1969), 335-340.
  4. R. Curto, C. Hernandez and E. de Oteyza, Contractive completions of Hankel partial contractions, J. Math. Anal. Appl. 203 (1996), 303-332. https://doi.org/10.1006/jmaa.1996.0382
  5. R. Curto, S. H. Lee and J. Yoon, Completion of Hankel partial contractions of extremal type, (preprint 2011).
  6. R. E. Curto and W. Y. Lee, Joint hyponormality of Toeplitz pairs, Memoirs Amer. Math. Soc., vol. 712, 2001.
  7. C. Davis, An extremal problem for extensions of a sesquilinear form, Linear Alg. Appl. 13 (1976), 91-102. https://doi.org/10.1016/0024-3795(76)90046-X
  8. C. Davis, W. M. Kahan, and H. F. Weinberger, Norm-preserving dilations and their application to optimal error bounds, SIAM J. Numer. Anal 19 (1982), 445-469. https://doi.org/10.1137/0719029
  9. C. Foias and A. E. Frazho, Redheffer products and the lifting of contractions on Hilbert space, J. Operator Th. 11 (1984), 193-196.
  10. I. S. Iohvidov, Hankel and Toeplitz Matrices and Forms: Algebraic Theory, Birkhauser-Verlag, Boston, 1982.
  11. C. R. Johnson and L. Rodman, Completion of partial matrices to contractions, J. Funct. Anal. 69 (1986), 260-267. https://doi.org/10.1016/0022-1236(86)90091-1
  12. C. R. Johnson and L. Rodman, Completion of Toeplitz partial contractions, SIAM J. Matrix Anal. Appl. 9 (1988), no. 2, 159-167. https://doi.org/10.1137/0609013
  13. S. Parrott, On a quotient norm and Sz.-Nagy-Foia»s lifting theorem, J. Funct. Anal. 30 (1978), 311-328. https://doi.org/10.1016/0022-1236(78)90060-5
  14. S. Power, The distance to upper triangular operators, Math. Proc. Cambridge Phil. Soc. 88(198), 327-329. https://doi.org/10.1017/S0305004100057637
  15. Y. L. Shmul'yan and R. N. Yanovskaya, Blocks of a contractive operator matrix (Russian), Izv. Vyssh. Uchebn. Zaved. Mat. 25(1981), 72-75
  16. Y. L. Shmul'yan and R. N. Yanovskaya, Blocks of a contractive operator matrix (English translation) Soviet Math. (Iz. VUZ) 25 (1981), 82-86.
  17. J. L. Smul'jan, An operator Hellinger integral, Mat. Sb. (N.S.) 49 (1959), 381-430 (in Russian).
  18. H. J. Woerdeman, Strictly contractive and positive completions for block matrices, Linear Alg. and Its Appl. 136 (1990), 63-105. https://doi.org/10.1016/0024-3795(90)90021-4
  19. Wolfram Research, Inc., Mathematica, Version 4.2, Wolfram Research Inc., Champaign, IL, 2002.