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Recursively generated weighted shifts and the subnormal completion problem

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References

  • [AbK] 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 

  • [Akh] N.I. Akhiezer, The Classical Moment Problem, Hafner Publ. Co., New York, 1965.

    Google Scholar 

  • [Ath] A. Athavale, On joint hyponormality of operators, Proc. Amer. Math. Soc. 103(1988), 417–423.

    Google Scholar 

  • [Atk] K. Atkinson, An Introduction to Numerical Analysis, Wiley, New York, 1978.

    Google Scholar 

  • [BeM] C. Berg and P.H. Maserick, Polynomially positive definite sequences, Math. Ann. 259(1982), 487–495.

    Google Scholar 

  • [Cla] K. Clancey, Seminormal operators, Lecture Notes in Math., vol. 742, Springer-Verlag, New York-Heidelberg-Berlin, 1979.

    Google Scholar 

  • [Con] J.B. Conway, Subnormal Operators, Pitman Publ. Co., London, 1981.

    Google Scholar 

  • [Cul] R.E. Curto, Quadratically hyponormal weighted shifts, Int. Eq. Op. Th. 13(1990), 49–66.

    Google Scholar 

  • [Cu2] R.E. Curto, Joint hyponormality: A bridge between hyponormality and subnormality, Proc. Symposia Pure Math. 51(1990), Part II, 69–91.

    Google Scholar 

  • [CuF1] R. Curto and L. Fialkow, Recursiveness, positivity, and truncated moment problems, Houston J. Math. 17(1991), 603–635.

    Google Scholar 

  • [CuF2] R. Curto and L. Fialkow, Quadratic hyponormality of recursively generated shifts, preprint 1992.

  • [CMX] R. Curto, P. Muhly and J. Xia, Hyponormal pairs of commuting operators, Operator Th.: Adv. Appl. 35(1988), 1–22.

    Google Scholar 

  • [CuP1] R. Curto and M. Putinar, Existence of non-subnormal polynomially hyponormal operators, Bull. Amer. Math. Soc. 25(1991), 373–378.

    Google Scholar 

  • [CuP2] R. Curto and M. Putinar, Nearly subnormal operators and moment problems, J. Funct. Anal., to appear.

  • [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 

  • [Fan] P. Fan, A note on hyponormal weighted shifts, Proc. Amer. Math. Soc. 92(1984), 271–272.

    Google Scholar 

  • [Hal] P.R. Halmos, Ten problems in Hilbert space, Bull. Amer. Math. Soc. 76(1970), 887–933.

    Google Scholar 

  • [Ioh] I.S. Iohvidov, Hankel and Toeplitz Matrices and Forms: Algebraic Theory, Birkhäuser-Verlag, Boston, 1982.

    Google Scholar 

  • [Jos1] A. Joshi, Hyponormal polynomials of monotone shifts, Ph. D. dissertation, Purdue University, 1971.

  • [Jos2] A. Joshi, Hyponormal polynomials of monotone shifts, Indian J. Pure Appl. Math. 6(1975), 681–686.

    Google Scholar 

  • [KoL] I. Koltracht and P. Lancaster, A definiteness test for Hankel matrices and their lower submatrices, Computing 39 (1987), 19–26.

    Google Scholar 

  • [KrN] 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 

  • [MaP] M. Martin and M. Putinar, Lectures on Hyponormal Operators, Operator Theory: Adv. Appl., vol. 39, Birkhäuser-Verlag, 1989.

  • [McCP] S. Cullough and V. Paulsen, A note on joint hyponormality, Proc. Amer. Math. Soc. 107(1989), 187–195.

    Google Scholar 

  • [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 

  • [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 

  • [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 

  • [Shi] A. Shields, Weighted shift operators and analytic function theory, Math. Surveys 13(1974), 49–128.

    Google Scholar 

  • [ShT] J.A. Shohat and J.D. Tamarkin, The Problem of Moments, Math. Surveys I, American Math. Soc., Providence, 1943.

    Google Scholar 

  • [Smu] J.L. Smul'jan, An operator Hellinger integral (Russian), Mat. Sb. 91 (1959), 381–430.

    Google Scholar 

  • [Sta] J. Stampfli, Which weighted shifts are subnormal, Pacific J. Math. 17(1966), 367–379.

    Google Scholar 

  • [Sto] M.H. Stone, Linear Transformations in Hilbert Space, Amer. Math. Soc., New York, 1932.

    Google Scholar 

  • [Xia] D. Xia, Spectral Theory of Hyponormal Operators, Operator Theory: Adv. Appl., vol. 10, Birkhäuser-Verlag, 1983.

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Both authors were partially supported by grants from NSF Raúl Curto was partially supported by a University of Iowa faculty scholar award

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Curto, R.E., Fialkow, L.A. Recursively generated weighted shifts and the subnormal completion problem. Integr equ oper theory 17, 202–246 (1993). https://doi.org/10.1007/BF01200218

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