Toeplitz-Berezin-type symbols and solutions of some operator equations

被引：0
作者：
Garayev, Mubariz [1 ]
Guediri, Hocine [1 ]
Sadraoui, Houcine [1 ]
机构：
[1] King Saud Univ, Coll Sci, Dept Math, Riyadh, Saudi Arabia
来源：
ILLINOIS JOURNAL OF MATHEMATICS | 2023年 / 67卷 / 03期
关键词：
EXTENDED EIGENVALUES; EIGENVECTORS; INVARIANT; EIGENSPACES; TRANSFORM; SPECTRUM; SPACE;
D O I：
10.1215/00192082-10597073
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We use Berezin-type symbols on the Dirichlet space D .Bn/ of the unit ball to investigate solutions of some Riccati operator equations of the form XAX C XB -CX -D = 0. In particular, we discuss the solvability of the operator equation XAX = AX in the set of all bounded Toeplitz operators acting on the Dirichlet space D .Bn/. Some other related questions, such as invariant subspaces, are also discussed.
引用
收藏
页码：423 / 442
页数：20
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