School of Mathematics, Statistics and Physics

Staff Profile

Dr Michael Dritschel

Reader in Pure Mathematics

Research

Research Interests

These are, broadly speaking, operator theory and operator algebras. Most recent work has been on abstract model theory for families of operators, and families of representations of algebras, as formulated by Jim Agler. Applications have included the study of model theory for the families of hyponormal contractions and -contractions. This work has been done in collaboration with Scott McCullough and Hugo Woerdeman.

Other areas of research interest include operator theory on Krein spaces (a type of indefinite metric space). Parts of this work was in collaboration with James Rovnyak.

Publications

  • Dritschel MA, Mccullough S. The failure of rational dilation on a triply connected domain. Journal of the American Mathematical Society 2005, 18(4), 873-918.
  • Dritschel MA, Marcantognini S, McCullough S. Interpolation in semigroupoid algebras. Journal fur die Reine und Angewandte Mathematik 2007, (606), 1-40.
  • Dritschel MA, Woerdeman HJ. Outer factorizations in one and several variables. Transactions of the American Mathematical Society 2005, 357(11), 4661-4679.
  • Dritschel MA, Mccullough SA. Boundary representations for families of representations of operator algebras and spaces. Journal of Operator Theory 2005, 53(1), 159-167.
  • Dritschel MA. On factorization of trigonometric polynomials. Integral Equations and Operator Theory 2004, 49(1), 11-42.
  • Dritschel MA, McCullough S. Model theory for hyponormal contractions. Integral Equations and Operator Theory 2000, 36(2), 182-192.
  • Dritschel, MA. A module approach to commutant lifting on Krein spaces. In: Alpay, D.; and Vinnikov, V, ed. Operator theory, system theory and related topics. Basel: Birkhäuser, 2001, pp.195-206.
  • Dritschel MA, McCullough S, Woerdeman HJ. Model theory for $\rho$-contractions, $\rho\le2$. Journal of Operator Theory 1999, 41(2), 321-350.
  • Dritschel MA, McCullough S. Test Functions, Kernels, Realizations and Interpolation. In: Bakonyi, M; Gheondea, A; Rovnyak, J, ed. Operator Theory, Structured Matrices, and Dilations: Tiberiu Constantinescu Memorial Volume. Bucharest: American Mathematical Society, 2007.
  • Dritschel Michael A., Woerdeman, Hugo J. Model theory and linear extreme points in the numerical radius unit ball. Memoirs of the American Mathematical Society. No. 615, 3rd of 4 numbers 1997, 129, viii+62.
  • Dritschel MA, Rovnyak J. Operators on indefinite inner product spaces. Fields Institute Monographs no.3, Amer.Math.Soc. Edited by Peter Lancaster 1996, 3, 141-232.
  • Dritschel, Michael A. Compact perturbations of operators on Kre\u\i n spaces. Harmonic analysis and operator theory (Caracas, 1994), Contemp. Math., Amer. Math. Soc., Providence, RI, 1995 1994, 189, 201-211.
  • Cowen, Carl C., Dritschel, Michael A., Penney, Richard C. Norms of Hadamard multipliers. SIAM J. Matrix Anal. Appl 1994, 15(1), 313-320.
  • Dritschel, Michael A. A method for constructing invariant subspaces for some operators on Kre\u\i n spaces. Operator extensions, interpolation of functions and related topics (Timi\c soara, 1992), Oper. Theory Adv. Appl., Birkhäuser, Basel 1993, 61, 85-113.
  • Dritschel, Michael A. The essential uniqueness property for operators on Kre\u\i n spaces. J. Funct. Anal. (Reviewer: Vladimir Derkach) 47B50 1993, 118(1), 198-248.
  • Dritschel, Michael A., Rovnyak, James. Julia operators and complementation in Kre\u\i n spaces. Indiana Univ. Math. J. (Reviewer: J. Bognár) 46C20 (46E22 47B50) 1991, 40(3), 885-901.
  • Dritschel, Michael A., Rovnyak, James. Extension theorems for contraction operators on Kre\u\i n spaces. Extension and interpolation of linear operators and matrix functions, Oper. Theory Adv. Appl., irkhäuser, Basel 1990, 47, 221-305.
  • Dritschel, Michael A. A lifting theorem for bicontractions on Kre\u\i n spaces. J. Funct. Anal. 89 1990, 1, 61-89.
  • Dritschel MA, ed. The Extended Field of Operator Theory. Basel: Birkhäuser Verlag, 2007.
  • Dritschel MA, Estévez D, Yakubovich D. Tests for complete K-spectral sets. Journal of Functional Analysis 2017, 273(3), 984-1019.
  • Dritschel MA, Jury MT, McCullough S. Dilations and Constrained Algebras. Operators and Matrices 2016, 10(4), 829-861.
  • Dritschel MA, Undrakh B. Rational dilation problems associated with constrained algebras. 2016. In Preparation.
  • Dritschel MA, Estévez D, Yakubovich D. Traces of analytic uniform algebras on subvarieties and test collections. Journal of the London Mathematical Society 2017, 95(2), 414-440.
  • Dritschel MA. Contractions and the commutant lifting theorem in Kreĭn spaces. In: Daniel Alpay, ed. Operator Theory. Basel: Springer, 2015, pp.219-239.
  • Dritschel MA, Bhattacharyya T, ed. Operator Algebras and Mathematical Physics. Basel: Birkhauser Basel, 2015.
  • Dritschel MA. Realizations via preorderings with application to the Schur class. 2015. In Preparation.
  • Dritschel MA, Ball JA, ter Elst AFM, Portal P, Potapov D, ed. Operator theory in harmonic and non-commutative analysis. Birkhäuser/Springer, Cham, 2014.
  • Dritschel MA, Battacharyya T, Todd CS. Completely Bounded Kernels. Acta Scientiarum Mathematicarum (Szeged) 2013, 79(1-2), 191-217.
  • Dritschel MA, Pickering J. Test functions in constrained interpolation. Transactions of the American Mathematical Society 2012, 364(11), 5589-5604.
  • Dritschel MA, Rovnyak J. The Operator Fejér-Riesz Theorem. In: Axler, S., Rosenthal, P., Sarason, D, ed. A Glimpse at Hilbert Space Operators: Paul R. Halmos in Memoriam. Basel, Switzerland: Birkhäuser Verlag, 2010, pp.223-254.
  • Dritschel, Michael A., Woerdeman, Hugo J. Model theory and linear extreme points in the numerical radius unit ball. Mem. Amer. Math. Soc 1997, 129.
  • Dritschel, Michael A., Rovnyak, James. Julia operators and complementation in Kre\u\i n spaces. Indiana Univ. Math. J. 40, no. 3, 885--901. (Reviewer: J. Bognár) 46C20 (46E22 47B50) 1991.
  • Dritschel MA, Estevez D, Yakubovich D. Resolvent criteria for similarity to a normal operator with spectrum on a curve. Journal of Mathematical Analysis and Applications 2018.