scholarly journals Commutative C*-Algebras Generated by Toeplitz Operators on the Super Unit Ball

2015 ◽  
Vol 26 (1) ◽  
pp. 363-397
Author(s):  
R. Quiroga-Barranco ◽  
A. Sánchez-Nungaray
Keyword(s):  
Unit Ball ◽  
Toeplitz Operators ◽  
C Algebras

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

scholarly journals Filters in C*-Algebras

2013 ◽  
Vol 65 (3) ◽  
pp. 485-509 ◽  
Author(s):  
Tristan Matthew Bice
Keyword(s):  
Unit Ball ◽  
Pure State ◽  
Positive Answer ◽  
The State ◽  
Natural Numbers ◽  
Cardinal Invariant ◽  
Calkin Algebra ◽  
C Algebras ◽  
Positive Elements ◽  
Singer Conjecture

AbstractIn this paper we analyze states on C*-algebras and their relationship to filter-like structures of projections and positive elements in the unit ball. After developing the basic theory we use this to investigate the Kadison–Singer conjecture, proving its equivalence to an apparently quite weak paving conjecture and the existence of unique maximal centred extensions of projections coming from ultrafilters on the natural numbers. We then prove that Reid's positive answer to this for q-points in fact also holds for rapid p-points, and that maximal centred filters are obtained in this case. We then show that consistently, such maximal centred filters do not exist at all meaning that, for every pure state on the Calkin algebra, there exists a pair of projections on which the state is 1, even though the state is bounded strictly below 1 for projections below this pair. Next, we investigate towers, using cardinal invariant equalities to construct towers on the natural numbers that do and do not remain towers when canonically embedded into the Calkin algebra. Finally, we show that consistently, all towers on the natural numbers remain towers under this embedding.

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 Compact Toeplitz operators on weighted harmonic Bergman spaces

1998 ◽  
Vol 64 (1) ◽  
pp. 136-148 ◽  
Author(s):  
Karel Stroethoff
Keyword(s):  
Unit Ball ◽  
Harmonic Functions ◽  
Toeplitz Operators ◽  
Bergman Spaces ◽  
Harmonic Bergman Spaces

AbstractWe consider the Bergman spaces consisting of harmonic functions on the unit ball in Rn that are squareintegrable with respect to radial weights. We will describe compactness for certain classes of Toeplitz operators on these harmonic Bergman spaces.

scholarly journals Algebras of Toeplitz Operators on the n-Dimensional Unit Ball

2018 ◽  
Vol 13 (2) ◽  
pp. 493-524 ◽  
Author(s):  
Wolfram Bauer ◽  
Raffael Hagger ◽  
Nikolai Vasilevski
Keyword(s):  
Unit Ball ◽  
Toeplitz Operators ◽  
Algebras Of Toeplitz Operators ◽  
Dimensional Unit

scholarly journals Characterizations of tripotents in JB*-triples

2006 ◽  
Vol 99 (1) ◽  
pp. 147 ◽  
Author(s):  
Remo V. Hügli
Keyword(s):  
Unit Ball ◽  
Partial Order ◽  
Facial Structure ◽  
Partial Isometries ◽  
C Algebras ◽  
Metric Characterization

The set $\mathcal{U}(A)$ of tripotents in a $\mathrm{JB}^*$-triple $A$ is characterized in various ways. Some of the characterizations use only the norm-structure of $A$. The partial order on $\mathcal{U}(A)$ as well as $\sigma$-finiteness of tripotents are described intrinsically in terms of the facial structure of the unit ball $A_1$ in $A$, i.e. without reference to the (pre-)dual of $A$. This extends similar results obtained in [6] and simplifies the metric characterization of partial isometries in $C^*$-algebras found in [1](cf. [8].

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