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Linear Combination of Two Composition Operators Between Different Fock Spaces


We investigate boundedness and compactness of linear combinations of two composition operators acting between different Fock spaces in several variables.

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  1. Choe, B.R., Izuchi, K.H., Koo, H.: Linear sums of two composition operators on the Fock spaces. J. Math. Anal. Appl. 369, 112–119 (2010)

    MathSciNet  Article  Google Scholar 

  2. Carswell, B., MacCluer, B.D., Schuster, A.: Composition operators on the Fock space. Acta Sci. Math. 69, 871–887 (2003)

    MathSciNet  MATH  Google Scholar 

  3. Cowen, C.C., MacCluer, B.D.: Composition Operators on Spaces of Analytic Functions. Studies in Advanced Mathematics. CRC Press, Boca Raton (1995)

    MATH  Google Scholar 

  4. Dai, J.: Topological components of the space of composition operators on Fock spaces. Complex Anal. Oper. Theor. 9, 201–212 (2015)

    MathSciNet  Article  Google Scholar 

  5. Hosokawa, T., Ohno, S.: Differences of composition operators on the Bloch spaces. J. Oper. Theor. 57, 229–242 (2007)

    MathSciNet  MATH  Google Scholar 

  6. Horn, R., Johnson, C.: Matrix Analysis. Cambridge University Press, Cambridge (1990)

    MATH  Google Scholar 

  7. Moorhouse, J.: Compact differences of composition operators. J. Funct. Anal. 219, 70–92 (2005)

    MathSciNet  Article  Google Scholar 

  8. Shapiro, J.H.: Compositions Operators and Classical Function Theory. Springer, New York (1993)

    Book  Google Scholar 

  9. Tien, P.T., Khoi, L.H.: Differences of weighted composition operators between the Fock spaces. Monatsh. Math. 188, 183–193 (2019)

    MathSciNet  Article  Google Scholar 

  10. Tien, P.T., Khoi, L.H.: Weighted composition operators between Fock spaces in several variables. Math. Nachr. 293, 1200–1220 (2020)

    MathSciNet  Article  Google Scholar 

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The authors are deeply grateful to the Referees for the useful comments and suggestions that led to the improvement of this paper.

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Correspondence to Pham Trong Tien.

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Lieu, P.T., Thu, D.T. & Tien, P.T. Linear Combination of Two Composition Operators Between Different Fock Spaces. Vietnam J. Math. 50, 151–159 (2022).

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  • Linear combination
  • Composition operator
  • Fock space

Mathematics Subject Classification (2010)

  • 47B33
  • 46E15