On compactness of products of Toeplitz operators
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912483487252480 |
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| author | Le, Trieu Rodriguez, Tomas Miguel Sahutoglu, Sonmez |
| author_facet | Le, Trieu Rodriguez, Tomas Miguel Sahutoglu, Sonmez |
| contents | We study compactness of product of Toeplitz operators with symbols continuous on the closure of the polydisc in terms of behavior of the symbols on the boundary. For certain classes of symbols $f$ and $g$, we show that $T_fT_g$ is compact if and only if $fg$ vanishes on the boundary. We provide examples to show that for more general symbols, the vanishing of $fg$ on the whole polydisc might not imply the compactness of $T_fT_g$. On the other hand, the reverse direction is closely related to the zero product problem for Toeplitz operators on the unit disc, which is still open. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_04869 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On compactness of products of Toeplitz operators Le, Trieu Rodriguez, Tomas Miguel Sahutoglu, Sonmez Functional Analysis Complex Variables 47B35, 32A36 We study compactness of product of Toeplitz operators with symbols continuous on the closure of the polydisc in terms of behavior of the symbols on the boundary. For certain classes of symbols $f$ and $g$, we show that $T_fT_g$ is compact if and only if $fg$ vanishes on the boundary. We provide examples to show that for more general symbols, the vanishing of $fg$ on the whole polydisc might not imply the compactness of $T_fT_g$. On the other hand, the reverse direction is closely related to the zero product problem for Toeplitz operators on the unit disc, which is still open. |
| title | On compactness of products of Toeplitz operators |
| topic | Functional Analysis Complex Variables 47B35, 32A36 |
| url | https://arxiv.org/abs/2401.04869 |