| Autor: |
Kunyu Guo, Xianfeng Zhao, Dechao Zheng |
| Zdroj: |
Arkiv foer Matematik; 2023, Vol. 61 Issue 2, p343-374, 32p |
| Abstrakt: |
This paper shows some new phenomenon in the spectral theory of Toeplitz operators on the Bergman space, which is considerably different from that of Toeplitz operators on the Hardy space. On the one hand, we prove that the spectrum of the Toeplitz operator with symbol z+p is always connected for every polynomial p with degree less than 3. On the other hand, we show that for each integer k greater than 2, there exists a polynomial p of degree k such that the spectrum of the Toeplitz operator with symbol z+p is a nonempty finite set. Then these results are applied to obtain a new class of non-hyponormal Toeplitz operators with bounded harmonic symbols on the Bergman space for which Weyl's theorem holds. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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