Reducing Subspaces of Toeplitz Operators Induced by a Class of Non-analytic Monomials over the Unit Ball  

作　　者：Yan Yue SHI Bo ZHANG Xu TANG Yu Feng LU 

机构地区：[1]School of Mathematical Sciences,Ocean University of China,Qingdao 266100,P.R.China [2]School of Mathematics and Information Sciences,Yantai University,Yantai 264005,P.R.China [3]School of Mathematical Sciences,Space Engineering University,Beijing 101416,P.R.China [4]School of Mathematical Sciences,Dalian University of Technology,Dalian 116024,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2024年第7期1767-1777,共11页数学学报（英文版）

基　　金：Supported by NSFC (Grant Nos. 12031002, 12371134);SDNSFC (Grant Nos. ZR2021MA015, ZR2020MA009)

摘　　要：In this paper,we describe the minimal reducing subspaces of Toeplitz operators induced by non-analytic monomials on the weighted Bergman spaces and Dirichlet spaces over the unit ball B_(2).It is proved that each minimal reducing subspace M is finite dimensional,and if dim M≥3,then M is induced by a monomial.Furthermore,the structure of commutant algebra v(T_(w)N_(z)N):={M^(*)_(w)NM_(z)N,M^(*)_(z)NM_(w)N}′is determined by N and the two dimensional minimal reducing subspaces of(T_(w)N_(z)N.We also give some interesting examples.

关 键 词：Reducing subspace operator-weighted shifts Toeplitz operator von Neumann algebra 

分 类 号：O177[理学—数学]