scholarly journals Eigenvalues of K-invariant Toeplitz Operators on Bounded Symmetric Domains

2021 ◽  
Vol 93 (3) ◽  
Author(s):  
Harald Upmeier
Keyword(s):  
Toeplitz Operators ◽  
Bergman Spaces ◽  
Weighted Bergman Spaces ◽  
Bounded Symmetric Domains

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 ) .

COMPACT OPERATORS AND THE PLURIHARMONIC BEREZIN TRANSFORM

2008 ◽  
Vol 19 (06) ◽  
pp. 645-669 ◽  
Author(s):  
WOLFRAM BAUER ◽  
KENRO FURUTANI
Keyword(s):  
Toeplitz Operators ◽  
Fock Space ◽  
Boundary Behavior ◽  
Bergman Spaces ◽  
Berezin Transform ◽  
Compact Operators ◽  
Point Of View ◽  
Weighted Bergman Spaces ◽  
Bounded Symmetric Domains

For a series of weighted Bergman spaces over bounded symmetric domains in ℂn, it has been shown by Axler and Zheng [1]; Englis [10] that the compactness of Toeplitz operators with bounded symbols can be characterized via the boundary behavior of its Berezin transform B a . In case of the pluriharmonic Bergman space, the pluriharmonic Berezin transform B ph fails to be one-to-one in general and even has non-compact operators in its kernel. From this point of view, perhaps surprisingly we show that via B ph the same characterization of compactness holds for Toeplitz operators on the pluriharmonic Fock space.

scholarly journals The Berezin Transform of Toeplitz Operators on the Weighted Bergman Space

2021 ◽  
Author(s):  
Cezhong Tong ◽  
Junfeng Li ◽  
Hicham Arroussi
Keyword(s):  
Bergman Space ◽  
Toeplitz Operators ◽  
Reproducing Kernel ◽  
Bergman Spaces ◽  
Essential Norm ◽  
Berezin Transform ◽  
Weighted Bergman Space ◽  
Weighted Bergman Spaces ◽  
Kernel Estimates ◽  
Berezin Transforms

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.

scholarly journals (m,λ)-Berezin Transform on the Weighted Bergman Spaces over the Polydisk

2016 ◽  
Vol 2016 ◽  
pp. 1-11
Author(s):  
Ran Li ◽  
Yufeng Lu
Keyword(s):  
Linear Operator ◽  
Bergman Space ◽  
Bounded Linear Operator ◽  
Toeplitz Operators ◽  
Bergman Spaces ◽  
Main Tool ◽  
Berezin Transform ◽  
Weighted Bergman Space ◽  
Weighted Bergman Spaces ◽  
Bounded Linear

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).

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