scholarly journals The commutants of certain Toeplitz operators on weighted Bergman spaces

2008 ◽  
Vol 348 (1) ◽  
pp. 1-11 ◽  
Author(s):  
Trieu Le
2021 ◽  
Vol 93 (3) ◽  
Author(s):  
Harald Upmeier

AbstractWe determine the eigenvalues of certain “fundamental” K-invariant Toeplitz type operators on weighted Bergman spaces over bounded symmetric domains $$D=G/K,$$ D = G / K , for the irreducible K-types indexed by all partitions of length $$r={\mathrm {rank}}(D)$$ r = rank ( D ) .


Author(s):  
Cezhong Tong ◽  
Junfeng Li ◽  
Hicham Arroussi

AbstractIn this paper, we obtain some interesting reproducing kernel estimates and some Carleson properties that play an important role. We characterize the bounded and compact Toeplitz operators on the weighted Bergman spaces with Békollé-Bonami weights in terms of Berezin transforms. Moreover, we estimate the essential norm of them assuming that they are bounded.


2016 ◽  
Vol 2016 ◽  
pp. 1-11
Author(s):  
Ran Li ◽  
Yufeng Lu

We prove that every bounded linear operator on weighted Bergman space over the polydisk can be approximated by Toeplitz operators under some conditions. The main tool here is the so-called(m,λ)-Berezin transform. In particular, our results generalized the results of K. Nam and D. C. Zheng to the case of operators acting onAλ2(Dn).


Filomat ◽  
2019 ◽  
Vol 33 (17) ◽  
pp. 5737-5741 ◽  
Author(s):  
Houcine Sadraoui

A bounded operator T on a Hilbert space is hyponormal if T*T-TT* is positive. We give a necessary condition for the hyponormality of Toeplitz operators on weighted Bergman spaces, for a certain class of radial weights, when the symbol is of the form f+g?, where both functions are analytic and bounded on the unit disk. We give a sufficient condition when f is a monomial.


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