Integral Equations and Operator Theory

, Volume 18, Issue 4, pp 369–426 | Cite as

Recursively generated weighted shifts and the subnormal completion problem, II

  • Raúl E. Curto
  • Lawrence A. Fialkow
Article

AMS (MOS) Subject Classification (1980)

Primary 47B37, 47B20, 44A60, 47B47, 47-04 Secondary 15A57, 15A48, 15-04, 52A40, 42C99 

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References

  1. [AK] N.I. Ahiezer and M. Krein, Some Questions in the Theory of Moments, Transl. Math. Monographs, vol. 2, American Math. Soc., Providence, 1962.Google Scholar
  2. [Akh] N.I. Akhiezer, The Classical Moment Problem, Hafner Publ. Co., New York, 1965.Google Scholar
  3. [Ath] A. Athavale, On joint hyponormality of operators, Proc. Amer. Math. Soc. 103(1988), 417–423.Google Scholar
  4. [Atk] K. Atkinson, An Introduction to Numerical Analysis, Wiley, New York, 1978.Google Scholar
  5. [BM] C. Berg and P.H. Maserick, Polynomially positive definite sequences, Math. Ann. 259(1982), 487–495.Google Scholar
  6. [Cla] K. Clancey, Seminormal operators, Lecture Notes in Math., vol. 742, Springer-Verlag, New York-Heidelberg-Berlin, 1979.Google Scholar
  7. [Con] J.B. Conway, Subnormal Operators, Pitman Publ. Co., London, 1981.Google Scholar
  8. [Cu1] R.E. Curto, Quadratically hyponormal weighted shifts, Int. Eq. Op. Th. 13(1990), 49–66.Google Scholar
  9. [Cu2] R.E. Curto, Joint hyponormality: A bridge between hyponormality and subnormality, Proc. Symposia Pure Math. 51(1990), Part II, 69–91.Google Scholar
  10. [Cu3] R.E. Curto, Polynomially hyponormal operators on Hilbert space, in Proceedings of ELAM VII, Revista Unión Mat. Arg. 37(1991), 29–56.Google Scholar
  11. [CF1] R. Curto and L. Fialkow, Recursiveness, positivity, and truncated moment problems, Houston J. Math. 17(1991), 603–635.Google Scholar
  12. [CF2] R. Curto and L. Fialkow, Recursively generated weighted shifts and the subnormal completion problem, Int. Eq. Op. Th. 17(1993), 202–246.Google Scholar
  13. [CMX] R. Curto, P. Muhly and J. Xia, Hyponormal pairs of commuting operators, Operator Th.: Adv. Appl. 35(1988), 1–22.Google Scholar
  14. [CP1] R. Curto and M. Putinar, Existence of non-subnormal polynomially hyponormal operators, Bull. Amer. Math. Soc. 25(1991), 373–378.Google Scholar
  15. [CP2] R. Curto and M. Putinar, Nearly subnormal operators and moment problems, J. Funct. Anal., to appear.Google Scholar
  16. [Dou] R.G. Douglas, On majorization, factorization and range inclusion of operators on Hilbert spaces, Proc. Amer. Math. Soc. 17(1966), 413–415.Google Scholar
  17. [Fan] P. Fan, A note on hyponormal weighted shifts, Proc. Amer. Math. Soc. 92(1984), 271–272.Google Scholar
  18. [Fia] L.A. Fialkow, The nonsingular support rank of a positive matrix, preprint 1992.Google Scholar
  19. [Hal] P.R. Halmos, Ten problems in Hilbert space, Bull. Amer. Math. Soc. 76(1970), 887–933.Google Scholar
  20. [Ioh] I.S. Iohvidov, Hankel and Toeplitz Matrices and Forms: Algebraic Theory, Birkhäuser-Verlag, Boston, 1982.Google Scholar
  21. [Jo1] A. Joshi, Hyponormal polynomials of monotone shifts, Ph. D. dissertation, Purdue University, 1971.Google Scholar
  22. [Jo2] A. Joshi, Hyponormal polynomials of monotone shifts, Indian J. Pure Appl. Math. 6(1975), 681–686.Google Scholar
  23. [KL] I. Koltracht and P. Lancaster, A definiteness test for Hankel matrices and their lower submatrices, Computing 39(1987), 19–26.Google Scholar
  24. [KN] M.G. Krein and A.A. Nudel'man, The Markov Moment Problem and Extremal Problems, Transl. Math. Monographs, vol. 50, American Math. Soc., Providence, 1977.Google Scholar
  25. [MP] M. Martin and M. Putinar, Lectures on Hyponormal Operators, Operator Theory: Adv. Appl., vol. 39, Birkhäuser-Verlag, 1989.Google Scholar
  26. [McCP] S. McCullough and V. Paulsen, A note on joint hyponormality, Proc. Amer. Math. Soc. 107(1989), 187–195.Google Scholar
  27. [Nar] F.J. Narcowich, R-operators II. On the approximation of certain operator-valued analytic functions and the Hermitian moment problem, Indiana Univ. Math. J. 26(1977), 483–513.Google Scholar
  28. [Put] C.R. Putnam, Commutation Properties of Hilbert Space Operators and Related Topics, Ergeb. der Math. und ihrer Grenz., vol. 36, Springer-Verlag, New York, 1967.Google Scholar
  29. [Sar] D. Sarason, Moment problems and operators in Hilbert space, Moments in Math., Proc. Symposia Applied Math., vol. 37, Amer. Math. Soc., 1987, pp. 54–70.Google Scholar
  30. [Shi] A. Shields, Weighted shift operators and analytic function theory, Math. Surveys 13(1974), 49–128.Google Scholar
  31. [ST] J.A. Shohat and J.D. Tamarkin, The Problem of Moments, Math. Surveys I, American Math. Soc., Providence, 1943.Google Scholar
  32. [Smu] J.L. Smul'jan, An operator Hellinger integral (Russian), Mat. Sb. 91(1959), 381–430.Google Scholar
  33. [Sta] J. Stampfli, Which weighted shifts are subnormal, Pacific J. Math. 17(1966), 367–379.Google Scholar
  34. [Sto] M.H. Stone, Linear Transformations in Hilbert Space, Amer. Math. Soc., New York, 1932.Google Scholar
  35. [Xia] D. Xia, Spectral Theory of Hyponormal Operators, Operator Theory: Adv. Appl., vol. 10, Birkhäuser-Verlag, 1983.Google Scholar

Copyright information

© Birkhäuser Verlag 1994

Authors and Affiliations

  • Raúl E. Curto
    • 1
  • Lawrence A. Fialkow
    • 2
  1. 1.Department of MathematicsThe University of IowaIowa City
  2. 2.Department of Mathematics and Computer ScienceSUNY College at New PaltzNew Paltz

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