scholarly journals Properties of Commutativity of Dual Toeplitz Operators on the Orthogonal Complement of Pluriharmonic Dirichlet Space over the Ball

2016 ◽  
Vol 2016 ◽  
pp. 1-9
Author(s):  
Yinyin Hu ◽  
Yufeng Lu ◽  
Tao Yu
Keyword(s):  
Sobolev Space ◽  
Unit Ball ◽  
Toeplitz Operators ◽  
Dirichlet Space ◽  
Orthogonal Complement ◽  
Pluriharmonic Functions

We completely characterize the pluriharmonic symbols for (semi)commuting dual Toeplitz operators on the orthogonal complement of the pluriharmonic Dirichlet space in Sobolev space of the unit ball. We show that, forfandgpluriharmonic functions,SfSg=SgSfon(Dh)⊥if and only iffandgsatisfy one of the following conditions:(1)bothfandgare holomorphic;(2)bothf¯andg¯are holomorphic;(3)there are constantsαandβ, both not being zero, such thatαf+βgis constant.

scholarly journals Toeplitz Operators on the Dirichlet Space of𝔹n

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
HongZhao Lin ◽  
YuFeng Lu
Keyword(s):  
Unit Ball ◽  
Toeplitz Operator ◽  
Toeplitz Operators ◽  
Dirichlet Space ◽  
Algebraic Properties ◽  
Commuting Problem

We study the algebraic properties of Toeplitz operators on the Dirichlet space of the unit ball𝔹n. We characterize pluriharmonic symbol for which the corresponding Toeplitz operator is normal or isometric. We also obtain descriptions of conjugate holomorphic symbols of commuting Toeplitz operators. Finally, the commuting problem of Toeplitz operators whose symbols are of the formzpz¯qϕ(|z|2)is studied.

Kernels and spectrum of Toeplitz operators on the Dirichlet space

2019 ◽  
Vol 472 (1) ◽  
pp. 894-919 ◽  
Author(s):  
Yongning Li ◽  
Ziliang Zhang ◽  
Dechao Zheng
Keyword(s):  
Toeplitz Operators ◽  
Dirichlet Space

Some Extreme Rays of the Positive Pluriharmonic Functions

1979 ◽  
Vol 31 (1) ◽  
pp. 9-16 ◽  
Author(s):  
Frank Forelli
Keyword(s):  
Unit Ball ◽  
Extreme Point ◽  
Extreme Points ◽  
Holomorphic Functions ◽  
Open Unit ◽  
Compact Open Topology ◽  
Open Unit Ball ◽  
Pluriharmonic Functions ◽  
Image Position ◽  
Extreme Rays

1.1. We will denote by B the open unit ball in Cn, and we will denote by H(B) the class of all holomorphic functions on B. LetThus N(B) is convex (and compact in the compact open topology). We think that the structure of N(B) is of interest and importance. Thus we proved in [1] that if(1.1)if(1.2)and if n≧ 2, then g is an extreme point of N(B). We will denote by E(B) the class of all extreme points of N(B). If n = 1 and if (1.2) holds, then as is well known g ∈ E(B) if and only if(1.3)

Complex Symmetric Toeplitz Operators on the Unit Polydisk and the Unit Ball

2019 ◽  
Vol 40 (1) ◽  
pp. 35-44 ◽  
Author(s):  
Cao Jiang ◽  
Xingtang Dong ◽  
Zehua Zhou
Keyword(s):  
Unit Ball ◽  
Toeplitz Operators ◽  
Unit Polydisk ◽  
Complex Symmetric
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