Dual Toeplitz Operators on the Sphere  

作　　者：Hocine GUEDIRI 

机构地区：[1]Department of Mathematics, College of Science, King Saud University

出　　处：《Acta Mathematica Sinica,English Series》2013年第9期1791-1808,共18页数学学报（英文版）

基　　金：Supported by King Saud University, Deanship of Scientific Research, College of Science Research Center

摘　　要：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.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.

关 键 词：Dual Toeplitz operator Hardy space of the unit sphere COMMUTING Brown-Halmos theorem spectral inclusion QUASINORMAL 

分 类 号：O177[理学—数学]