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Model theory for hyponormal contractions

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Abstract

Agler's abstract model theory is applied to the family of hyponormal contractions. A sufficient condition for an operator to be extremal in this family is given, and this is used to show that the boundary, or smallest model, for the family is the whole family.

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References

  1. Jim Agler,An abstract approach to model theory, Surveys of some recent results in operator theory, Volume II, Pitman Research Notes in Mathematics Series 192, John Wiley and Sons, New York, 1988, pp. 1–23; MR 90a:47016.

    Google Scholar 

  2. R. E. Curto,Joint hyponormality: a bridge between hyponormality and subnormality, Operator theory: operator algebras and applications, Part 2 (Durham, NH, 1988), Proc. Sympos. Pure Math., 51, Part 2, Amer. Math. Soc., Providence, RI, 1990, pp. 69–91; MR 91k:47049.

    Google Scholar 

  3. R. E. Curto,Quadratically hyponormal weighted shifts, Integral Equations Operator Theory13 (1990), 49–66; MR 90k:47061.

    Google Scholar 

  4. M. Martin and M. Putinar,Lectures on hyponormal operators, Operator Theory: Advances and Applications, Vol. 39, Birkhäuser Verlag, Basel, 1989; MR 91c:47041.

    Google Scholar 

  5. M. A. Dritschel, S. McCullough, and H. J. Woerdeman,Model Theory for ρ-contractions, ρ≤2, J. Operator Theory41 (1999), 321–350.

    Google Scholar 

  6. D. X. Xia,Spectral theory of hyponormal operators, Operator Theory: Advances and Applications, Vol. 10, Birkhäuser Verlag, Basel, 1983; MR 87j:47036.

    Google Scholar 

  7. D. X. Xia,Hyponormal operators with finite rank self-commutators and quadrature domains., J. Math. Anal. Appl.203 (1996), 540–559; MR 97i:47035.

    Google Scholar 

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Dritschel, M.A., McCullough, S. Model theory for hyponormal contractions. Integr equ oper theory 36, 182–192 (2000). https://doi.org/10.1007/BF01202093

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