scholarly journals Formulas for Singular Values of Hankel Operators and Mixed Hankel-Toeplitz Operators Using Lifting Technique on the Left Shift Invariant Subspace

2000 ◽  
Vol 36 (9) ◽  
pp. 780-788
Author(s):  
Yoshito OHTA
Keyword(s):  
Invariant Subspace ◽  
Toeplitz Operators ◽  
Singular Values ◽  
Hankel Operators ◽  
Lifting Technique ◽  
Left Shift

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 On a class of shift-invariant subspaces of the Drury-Arveson space

2018 ◽  
Vol 5 (1) ◽  
pp. 1-8
Author(s):  
Nicola Arcozzi ◽  
Matteo Levi
Keyword(s):  
Invariant Subspace ◽  
Invariant Subspaces ◽  
Hankel Operators ◽  
Taylor Coefficients ◽  
The Right ◽  
Arveson Space

Abstract In the Drury-Arveson space, we consider the subspace of functions whose Taylor coefficients are supported in a set Y⊂ ℕd with the property that ℕ\X + ej ⊂ ℕ\X for all j = 1, . . . , d. This is an easy example of shift-invariant subspace, which can be considered as a RKHS in is own right, with a kernel that can be explicitly calculated for specific choices of X. Every such a space can be seen as an intersection of kernels of Hankel operators with explicit symbols. Finally, this is the right space on which Drury’s inequality can be optimally adapted to a sub-family of the commuting and contractive operators originally considered by Drury.

Products of Toeplitz operators and Hankel operators

2014 ◽  
Vol 220 (3) ◽  
pp. 277-292 ◽  
Author(s):  
Yufeng Lu ◽  
Linghui Kong
Keyword(s):  
Toeplitz Operators ◽  
Hankel Operators

scholarly journals Nearly Invariant Subspaces with Applications to Truncated Toeplitz Operators

2020 ◽  
Vol 14 (8) ◽  
Author(s):  
Ryan O’Loughlin
Keyword(s):  
Hardy Space ◽  
Toeplitz Operator ◽  
Invariant Subspace ◽  
Toeplitz Operators ◽  
Invariant Subspaces ◽  
Decomposition Theorem ◽  
Truncated Toeplitz Operator ◽  
Finite Defect ◽  
Vector Valued

AbstractIn this paper we first study the structure of the scalar and vector-valued nearly invariant subspaces with a finite defect. We then subsequently produce some fruitful applications of our new results. We produce a decomposition theorem for the vector-valued nearly invariant subspaces with a finite defect. More specifically, we show every vector-valued nearly invariant subspace with a finite defect can be written as the isometric image of a backwards shift invariant subspace. We also show that there is a link between the vector-valued nearly invariant subspaces and the scalar-valued nearly invariant subspaces with a finite defect. This is a powerful result which allows us to gain insight in to the structure of scalar subspaces of the Hardy space using vector-valued Hardy space techniques. These results have far reaching applications, in particular they allow us to develop an all encompassing approach to the study of the kernels of: the Toeplitz operator, the truncated Toeplitz operator, the truncated Toeplitz operator on the multiband space and the dual truncated Toeplitz operator.

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