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Factorizations of Characteristic Functions of Iterated Liftings

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Abstract

We obtain a factorization of the characteristic function of a contractive two-step iterated lifting in terms of the characteristic functions of constituent liftings of the iterated lifting and the Julia–Halmos matrix. We also give an expression for the characteristic function of the minimal part of a contractive two-step iterated lifting as a restriction of the product of the characteristic functions of constituent liftings of the iterated lifting.

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References

  1. Arveson, W.: Subalgebras of \(C^*\)-algebras. III .Multivariable operator theory. Acta Math. 181(2), 159–228 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  2. Ando, T.: Unitary dilation for a triple of commuting contractions. Bull. Acad. Polon. Sci. Sr. Sci. Math. Astron. Phys. 24(10), 851–853 (1976)

    MathSciNet  MATH  Google Scholar 

  3. Bhattacharyya, T., Eschmeier, J., Sarkar, J.: Characteristic function of a pure commuting contractive tuple, Integral Equations Operator Theory 53(1), 23–32 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  4. Benhida, C., Timotin, D.: Characteristic functions for multicontractions and automorphisms of the unit ball, Integral Equations Operator Theory 57(2), 153–166 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  5. Dey, S., Gohm, R.: Characteristic functions for ergodic tuples, Integral Equations Operator Theory 58, 43–63 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  6. Dey, S., Gohm, R.: Characteristic functions of liftings, J. Oper. Theory 65(1), 17–45 (2011)

    MathSciNet  MATH  Google Scholar 

  7. Dey, S., Gohm, R., Haria, K.J.: Functional models and minimal contractive liftings, Complex Anal. Oper. Theory 9(4), 933–955 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  8. Dey, S., Gohm, R., Haria, K.J.: Characteristic functions of liftings-II, Oper. Matrices 12(2), 579–601 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  9. Haria, K.J., Maji, A., Sarkar, J.: Factorizations of characteristic functions. J. Operator Theory 77(2), 377–390 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  10. Popescu, G.: Characteristic functions for infinite sequences of noncommuting operators, J. Oper. Theory 22(1), 51–71 (1989)

    MathSciNet  MATH  Google Scholar 

  11. Popescu, G.: Characteristic functions and joint invariant subspaces, J. Funct. Anal. 237(1), 277–320 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  12. Popescu, G.: Isometric dilations for infinite sequences of noncommuting operators, Trans. Am. Math. Soc. 316(2), 523–536 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  13. Popescu, G.: Multi-analytic operators on Fock spaces, Math. Ann. 303(1), 31–46 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  14. Popescu, G.: Multi-analytic operators and some factorization theorems, Indiana Univ. Math. J. 38(3), 693–710 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  15. Popescu, G.: Operator theory on noncommutative domains, Mem. Am. Math. Soc. 205(964), 124 2010)

    MathSciNet  MATH  Google Scholar 

  16. Sz-Nagy, B., Foias, C.: Forme triangulaire d’une contraction et factorisation de la fonction caractéristique, Acta Sci. Math. (Szeged) 28, 201–212 (1967)

    MathSciNet  MATH  Google Scholar 

  17. Sz-Nagy, B., Foiaş, C., Bercovici, H., Kérchy, L.: Harmonic Analysis of Operators on Hilbert Space, 2nd edn, revised and enlarged edn. Universitext, Springer, New York (2010)

  18. Timotin, D.: Note on a Julia operator related to model spaces, In: Mashreghi, J., Fricain, E., Ross, W. (eds.) Invariant Subspaces of the Shift Operator, 247–254, Contemporary Mathematics, 638, Centre de Recherches Mathematiques (CRM) Proceedings. American Mathematical Society, Providence, RI (2015)

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Acknowledgements

The first author was supported by the Department of Mathematics, IIT Bombay, India. The second author was supported by SERB MATRICS Grant Number MTR/2018/000343.

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Authors and Affiliations

  1. Stat-Math Unit, Indian Statistical Institute, R. V. College Post, Bangalore, 560059, India

    Neeru Bala

  2. Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai, 400076, India

    Santanu Dey & M. N. Reshmi

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  1. Neeru Bala
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  2. Santanu Dey
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  3. M. N. Reshmi
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All authors contributed to the research work. All authors wrote the main manuscript text.

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Correspondence to Santanu Dey.

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Communicated by Tirthankar Bhattacharyya.

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Bala, N., Dey, S. & Reshmi, M.N. Factorizations of Characteristic Functions of Iterated Liftings. Complex Anal. Oper. Theory 17, 79 (2023). https://doi.org/10.1007/s11785-023-01370-8

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