A sufficient condition for hyponormal Toeplitz operators on the Bergman space
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In this paper we consider the sufficient condition for hyponormal Toeplitz operators $T_{\varphi}$ with non-harmonic symbols $$\varphi(z)=\sum_{\ell=1}^{k}a_{\ell}z^{m_{\ell}}\overline{z}^{n_{\ell}}$$ with $m_{\ell}-n_{\ell}=\delta > 0$ for all $1 \le {\ell} \le k$, and $a_{\ell} \in \mathbb C$ on the Bergman spaces. In particular, we will observe the characteristics of the hyponormality of the Toeplitz operators $T_{\varphi}$ according to the positional relationship of the coefficients $a_{\ell}$'s.
Abstract
In this paper we consider the sufficient condition for hyponormal Toeplitz operators $T_{\varphi}$ with non-harmonic symbols $$\varphi(z)=\sum_{\ell=1}^{k}a_{\ell}z^{m_{\ell}}\overline{z}^{n_{\ell}}$$ with $m_{\ell}-n_{\ell}=\delta > 0$ for all $1 \le {\ell} \le k$, and $a_{\ell} \in \mathbb C$ on the Bergman spaces. In particular, we will observe the characteristics of the hyponormality of the Toeplitz operators $T_{\varphi}$ according to the positional relationship of the coefficients $a_{\ell}$'s.
참고문헌 (14)
- S. Axler, "Surveys of some recent results in operator theory, Vol. I", pp.1~50 (1988), Longman Sci. Tech
- C. C. Cowen, "Surveys of some recent results in operator theory, Vol. I", pp.155~167 (1988), Longman Sci. Tech
- M. Fleeman, "Hyponormal Toeplitz operators with non-harmonic symbol acting on the Bergman space", Oper. Matrices, 13(1), pp.61~83 (2019)[DOI]
- H. Hedenmalm, "Theory of Bergman Spaces" (2000), Springer
- I. S. Hwang, "Hyponormal Toeplitz operators on the Bergman space", J. Korean Math. Soc, 42(2), pp.387~403 (2005)[DOI]
- I. S. Hwang, "Hyponormal Toeplitz operators on the Bergman spaces. II", Bull. Korean Math. Soc, 44(3), pp.517~522 (2007)[DOI]
- S. Kim, "Hyponormality of Toeplitz operators with non-harmonic symbols on the Bergman spaces", J. Inequal. Appl, (67), pp.13~ (2021)[DOI]
- S. Kim, "Hyponormal Toeplitz operators with non-harmonic symbols on the weighted Bergman spaces", Ann. Funct. Anal, 14(1), pp.14~ (2023)[DOI]
- S. Kim, "Remarks on hyponormal Toeplitz operators with nonharmonic symbols", Open Math, 21(1), pp.20230114~ (2023)[DOI]
- E. Ko, "Remarks on hyponormal Toeplitz operators on the weighted Bergman spaces", Complex Anal. Oper. Theory, 14(8), pp.83~ (2020)[DOI]
- T. Le, "Hyponormal Toeplitz operators on weighted Bergman spaces", Integral Transforms Spec. Funct, 32(5-8), pp.560~567 (2021)[DOI]
- Y. Lu, "Commutativity and hyponormality of Toeplitz operators on the weighted Bergman space", J. Korean Math. Soc, 46(3), pp.621~642 (2009)[DOI]
- H. Sadraoui, "Hyponormality of Toeplitz operators and composition operators", pp.1992
- B. Simanek, "Hyponormal Toeplitz operators with non-harmonic algebraic symbol", Anal. Math. Phys, 9(4), pp.1613~1626 (2019)[DOI]