Gu, Dinggui The numerical range of Toeplitz operator on the polydisk. (English) Zbl 1176.30102 Abstr. Appl. Anal. 2009, Article ID 757964, 8 p. (2009). Summary: The numerical range and normality of Toeplitz operators acting on the Bergman space and the pluriharmonic Bergman space on the polydisk is investigated in this paper. Cited in 1 Document MSC: 30H10 Hardy spaces 30H20 Bergman spaces and Fock spaces 32A36 Bergman spaces of functions in several complex variables 32A37 Other spaces of holomorphic functions of several complex variables (e.g., bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) 47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators PDF BibTeX XML Cite \textit{D. Gu}, Abstr. Appl. Anal. 2009, Article ID 757964, 8 p. (2009; Zbl 1176.30102) Full Text: DOI EuDML OpenURL References: [1] K. E. Gustafson and D. K. M. Rao, Numerical Range: The Field of Values of Linear Operators and Matrices, Universitext, Springer, New York, NY, USA, 1997. [2] J. K. Thukral, “The numerical range of a Toeplitz operator with harmonic symbol,” Journal of Operator Theory, vol. 34, no. 2, pp. 213-216, 1995. · Zbl 0851.47020 [3] A. Brown and P. R. Halmos, “Algebraic properties of Toeplitz operators,” Journal für die Reine und Angewandte Mathematik, vol. 213, pp. 89-102, 1963. · Zbl 0116.32501 [4] E. M. Klein, “The numerical range of a Toeplitz operator,” Proceedings of the American Mathematical Society, vol. 35, pp. 101-103, 1972. · Zbl 0268.47029 [5] B. R. Choe and Y. J. Lee, “The numerical range and normality of Toeplitz operators,” Far East Journal of Mathematical Sciences, pp. 71-80, 2001. · Zbl 0987.47012 [6] S. Stević, “Weighted integrals of holomorphic functions on the polydisc. II,” Zeitschrift für Analysis und ihre Anwendungen, vol. 23, no. 4, pp. 775-782, 2004. · Zbl 1067.32003 [7] S. Stević, “A note on a theorem of Zhu on weighted Bergman projections on the polydisc,” Houston Journal of Mathematics, vol. 34, no. 4, pp. 1233-1241, 2008. · Zbl 1166.32001 [8] S. Stević, “Holomorphic functions on the mixed norm spaces on the polydisc,” Journal of the Korean Mathematical Society, vol. 45, no. 1, pp. 63-78, 2008. · Zbl 1137.32003 [9] K. H. Zhu, “The Bergman spaces, the Bloch space, and Gleason/s problem,” Transactions of the American Mathematical Society, vol. 309, no. 1, pp. 253-268, 1988. · Zbl 0657.32002 [10] K. H. Zhu, “Weighted Bergman projections on the polydisc,” Houston Journal of Mathematics, vol. 20, no. 2, pp. 275-292, 1994. · Zbl 0818.32007 [11] J. Lee, “An invariant mean value property in the polydisc,” Illinois Journal of Mathematics, vol. 42, no. 3, pp. 406-419, 1998. · Zbl 0902.31002 [12] Y. J. Lee and K. Zhu, “Some differential and integral equations with applications to Toeplitz operators,” Integral Equations and Operator Theory, vol. 44, no. 4, pp. 466-479, 2002. · Zbl 1023.45005 [13] B. R. Choe and K. S. Nam, “Note on commuting Toeplitz operators on the pluriharmonic Bergman space,” Journal of the Korean Mathematical Society, vol. 43, no. 2, pp. 259-269, 2006. · Zbl 1103.47018 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.