Generalized Hankel operators on the Fock space

2009 ◽  
Vol 282 (12) ◽  
pp. 1811-1826 ◽  
Author(s):  
Georg Schneider ◽  
Kristan A. Schneider
Keyword(s):  
Fock Space ◽  
Hankel Operators

Generalized Hankel operators on the Fock space II

2011 ◽  
Vol 284 (14-15) ◽  
pp. 1967-1984 ◽  
Author(s):  
Georg Schneider ◽  
Kristan Schneider
Keyword(s):  
Fock Space ◽  
Hankel Operators

Products of Hankel operators on the Fock space

2019 ◽  
Vol 277 (8) ◽  
pp. 2644-2663 ◽  
Author(s):  
Pan Ma ◽  
Fugang Yan ◽  
Dechao Zheng ◽  
Kehe Zhu
Keyword(s):  
Fock Space ◽  
Hankel Operators

scholarly journals Boundedness and Compactness of Hankel Operators on Large Fock Space

2022 ◽  
Vol 2022 ◽  
pp. 1-12
Author(s):  
Xiaofeng Wang ◽  
Zhicheng Zeng
Keyword(s):  
Lebesgue Space ◽  
Fock Space ◽  
Hankel Operators ◽  
Weighted Lebesgue Space ◽  
Bmo Spaces ◽  
Complex Valued

We introduce the BMO spaces and use them to characterize complex-valued functions f such that the big Hankel operators H f and H f ¯ are both bounded or compact from a weighted large Fock space F p ϕ into a weighted Lebesgue space L p ϕ when 1 ≤ p < ∞ .

Operators induced by weighted Toeplitz and weighted Hankel operators

2018 ◽  
Vol 48 (2) ◽  
pp. 99-111
Author(s):  
Gopal Datt ◽  
Anshika Mittal
Keyword(s):  
Hankel Operators

The range of block Hankel operators

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3237-3243
Author(s):  
In Hwang ◽  
In Kim ◽  
Sumin Kim
Keyword(s):  
Hardy Space ◽  
Invariant Subspace ◽  
Hankel Operators ◽  
Coprime Factorization ◽  
Backward Shift ◽  
Vector Valued

In this note we give a connection between the closure of the range of block Hankel operators acting on the vector-valued Hardy space H2Cn and the left coprime factorization of its symbol. Given a subset F ? H2Cn, we also consider the smallest invariant subspace S*F of the backward shift S* that contains F.

scholarly journals Lebesgue Decomposition of Non-Commutative Measures

2020 ◽  
Author(s):  
Michael T Jury ◽  
Robert T W Martin
Keyword(s):  
Hilbert Space ◽  
Reproducing Kernel ◽  
Fock Space ◽  
Reproducing Kernel Hilbert Space ◽  
Semigroup Algebra ◽  
Space Theory ◽  
Lebesgue Decomposition ◽  
Sesquilinear Forms ◽  
Positive Linear Functionals ◽  
Algebra Theory

Abstract We extend the Lebesgue decomposition of positive measures with respect to Lebesgue measure on the complex unit circle to the non-commutative (NC) multi-variable setting of (positive) NC measures. These are positive linear functionals on a certain self-adjoint subspace of the Cuntz–Toeplitz $C^{\ast }-$algebra, the $C^{\ast }-$algebra of the left creation operators on the full Fock space. This theory is fundamentally connected to the representation theory of the Cuntz and Cuntz–Toeplitz $C^{\ast }-$algebras; any *−representation of the Cuntz–Toeplitz $C^{\ast }-$algebra is obtained (up to unitary equivalence), by applying a Gelfand–Naimark–Segal construction to a positive NC measure. Our approach combines the theory of Lebesgue decomposition of sesquilinear forms in Hilbert space, Lebesgue decomposition of row isometries, free semigroup algebra theory, NC reproducing kernel Hilbert space theory, and NC Hardy space theory.

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