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http://dx.doi.org/10.4134/BKMS.b150974

ISOMETRIC WEIGHTED COMPOSITION OPERATORS ON THE FOCK SPACE OF ℂN  

Zhao, Liankuo (School of Mathematics and Computer Science Shanxi Normal University)
Publication Information
Bulletin of the Korean Mathematical Society / v.53, no.6, 2016 , pp. 1785-1794 More about this Journal
Abstract
This paper gives complete characterization for isometric weighted 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.
Keywords
Fock space; weighted composition operator; isometric; unitary;
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1 R. F. Allen and F. Colonna, On the isometric composition operators on the Bloch space in $C^n$, J. Math. Anal. Appl. 355 (2009), no. 2, 675-688.   DOI
2 J. Bonet, M. Lindstrom, and E. Wolf, Isometric weighted composition operators on weighted Banach spaces of type $H^{\infty}$, Proc. Amer. Math. Soc. 136 (2008), no. 12, 4267-4273.   DOI
3 L. Feng and L. Zhao, A note on weighted composition operators on the Fock space, Commun. Math. Res. 31 (2015), no. 3, 281-284.
4 F. Forelli, The isometries of $H^p$, Canad. J. Math. 16 (1964), 721-728.   DOI
5 C. J. Kolaski, Isometries of weighted Bergman spaces, Canad. J. Math. 34 (1982), no. 4, 910-915.   DOI
6 R. Kumar and J. R. Partington, Weighted composition operators on Hardy and Bergman spaces, Recent advances in operator theory, operator algebras, and their applications, 157-167, Operator Theory: Advances and Applications 153, Birkhauser, Basel, 2005.
7 T. Le, Normal and isometric weighted composition operators on the Fock space, Bull. Lond. Math. Soc. 46 (2014), no. 4, 847-856.   DOI
8 M. J. Martin and D. Vukotic, Isometries of the Dirichlet space among the composition operators, Proc. Amer. Math. Soc. 134 (2006), no. 6, 1701-1705.   DOI
9 M. J. Martin and D. Vukotic, Isometries of the Bloch space among the composition operators, Bull. Lond. Math. Soc. 39 (2007), no. 1, 151-155.   DOI
10 M. J. Martin and D. Vukotic, Isometries of some classical function spaces among the composition operators, Recent Advances in Operator-related Function Theory, 133-138, Contemporary Mathematics, 393, Amer. Math. Soc., Providence, RI, 2006.
11 W. Rudin, Function Theory in the Unit Ball of ${\mathbb{C}}^n$, New-York, Springer-Verlag, 1980.
12 L. Zhao, Unitary weighted composition operators on the Fock space of ${\mathbb{C}}^n$, Complex Anal. Oper. Theory 8 (2014), no. 2, 581-590.   DOI
13 L. Zhao, Invertible weighted composition operators on the Fock space of ${\mathbb{C}}^N$, J. Funct. Spaces 2015 (2015), Art. ID 250358, 5 pp.
14 L. Zhao, A note on invertible weighted composition operators on the Fock pace of ${\mathbb{C}}^N$, J. Math. Res. Appl. 36 (2016), no. 3, 359-362.