Abstract
Dual Toeplitz operators on the Hardy space of the unit circle are anti-unitarily equivalent to Toeplitz operators. In higher dimensions, for instance on the unit sphere, dual Toeplitz operators might behave quite differently and, therefore, seem to be a worth studying new class of Toeplitz-type operators. The purpose of this paper is to introduce and start a systematic investigation of dual Toeplitz operators on the orthogonal complement of the Hardy space of the unit sphere in ℂn. In particular, we establish a corresponding spectral inclusion theorem and a Brown-Halmos type theorem. On the other hand, we characterize commuting dual Toeplitz operators as well as normal and quasinormal ones.
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Supported by King Saud University, Deanship of Scientific Research, College of Science Research Center
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Guediri, H. Dual Toeplitz operators on the sphere. Acta. Math. Sin.-English Ser. 29, 1791–1808 (2013). https://doi.org/10.1007/s10114-013-1717-z
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DOI: https://doi.org/10.1007/s10114-013-1717-z
Keywords
- Dual Toeplitz operator
- Hardy space of the unit sphere
- commuting
- Brown-Halmos theorem
- spectral inclusion
- quasinormal