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Isometric weighted composition operators on the Fock space of $\mathbb{C}^N$

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This paper gives complete characterization for isometric wei\-ghted composition operators on the Fock space of $\mathbb{C}^N$. The main result shows that an isometric weighted composition operator on the Fock space of $\mathbb{C}^N$ is a unitary operator.

Abstract

This paper gives complete characterization for isometric wei\-ghted composition operators on the Fock space of $\mathbb{C}^N$. The main result shows that an isometric weighted composition operator on the Fock space of $\mathbb{C}^N$ is a unitary operator.

참고문헌 (14)

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  3. L. Feng, "A note on weighted composition operators on the Fock space", Commun. Math. Res, 31(3), pp.281~284 (2015)
  4. F. Forelli, "The isometries of Hp", Canad. J. Math, 16, pp.721~728 (1964)
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  6. R. Kumar, "Recent advances in operator theory, operator algebras, and their applications", pp.157~167 (2005), Birkhauser
  7. T. Le, "Normal and isometric weighted composition operators on the Fock space", Bull. Lond. Math. Soc, 46(4), pp.847~856 (2014)
  8. M. J. Mart´ın, "Isometries of the Dirichlet space among the composition operators", Proc. Amer. Math. Soc, 134(6), pp.1701~1705 (2006)
  9. M. J. Mart´ın, "Isometries of the Bloch space among the composition operators", Bull. Lond. Math. Soc, 39(1), pp.151~155 (2007)
  10. M. J. Martın, "Recent Advances in Operator-related Function Theory", pp.133~138 (2006), Amer. Math. Soc.
  11. W. Rudin, "Function Theory in the Unit Ball of Cn" (1980), Springer-Verlag
  12. L. Zhao, "Unitary weighted composition operators on the Fock space of Cn", Complex Anal. Oper. Theory, 8(2), pp.581~590 (2014)
  13. L. Zhao, "Invertible weighted composition operators on the Fock space of CN", J. Funct. Spaces, 2015, pp.5~ (2015)
  14. L. Zhao, "A note on invertible weighted composition operators on the Fock pace of CN", J. Math. Res. Appl, 36(3), pp.359~362 (2016)

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