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Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Products of Toeplitz and Hankel operators on the Bergman space in the polydisk

100%
Sobolewski P.
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
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2018
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tom 72
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nr 2
EN
In this paper we obtain a condition for analytic square integrable functions \(f,g\) which guarantees the boundedness of products of the Toeplitz operators \(T_fT_{\bar g}\) densely defined on the Bergman space in the polydisk. An analogous condition for the products of the Hankel operators \(H_fH^*_g\) is also given.
2
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On the Commutativity of a Certain Class of Toeplitz Operators

100%
Louhichi I., Randriamahaleo F., Zakariasy L.
Concrete Operators
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2015
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tom 2
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nr 1
EN
One of the major goals in the theory of Toeplitz operators on the Bergman space over the unit disk D in the complex place C is to completely describe the commutant of a given Toeplitz operator, that is, the set of all Toeplitz operators that commute with it. Here we shall study the commutants of a certain class of quasihomogeneous Toeplitz operators defined on the harmonic Bergman space.
3
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Toeplitz operators and Wiener-Hopf factorisation: an introduction

80%
Câmara M. C.
Concrete Operators
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2017
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tom 4
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nr 1
130-145
EN
Wiener-Hopf factorisation plays an important role in the theory of Toeplitz operators. We consider here Toeplitz operators in the Hardy spaces Hp of the upper half-plane and we review how their Fredholm properties can be studied in terms of a Wiener-Hopf factorisation of their symbols, obtaining necessary and sufficient conditions for the operator to be Fredholm or invertible, as well as formulae for their inverses or one-sided inverses when these exist. The results are applied to a class of singular integral equations in L−1(ℝ)
4
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Properties of two variables Toeplitz type operators

70%
Król-Klimkowska E., Ptak M.
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
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2016
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tom 15
EN
The investigation of properties of generalized Toeplitz operators with respect to the pairs of doubly commuting contractions (the abstract analogue of classical two variable Toeplitz operators) is proceeded. We especially concentrate on the condition of existence such a non-zero operator. There are also presented conditions of analyticity of such an operator.
5
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Outer factorization of operator valued weight functions on the torus

70%
Cheng R.
Studia Mathematica
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1994
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tom 110
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nr 1
19-34
EN
An exact criterion is derived for an operator valued weight function $W(e^{is},e^{it})$ on the torus to have a factorization $W(e^{is},e^{it}) = Φ(e^{is},e^{it})*Φ(e^{is},e^{it})$, where the operator valued Fourier coefficients of Φ vanish outside of the Helson-Lowdenslager halfplane $Λ = {(m,n) ∈ ℤ^2: m ≥ 1} ∪ {(0,n): n ≥ 0}$, and Φ is "outer" in a related sense. The criterion is expressed in terms of a regularity condition on the weighted space $L^2(W)$ of vector valued functions on the torus. A logarithmic integrability test is also provided. The factor Φ is explicitly constructed in terms of Toeplitz operators and other structures associated with W. The corresponding version of Szegö's infimum is given.
6
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On the reflexivity of multigenerator algebras

42%
Ptak M.
Instytut Matematyczny Polskiej Akademii Nauk
EN
CONTENTS 1. Introduction...................................................................................................5 2. N-tuples of linear transformations in finite-dimensional space......................8 3. Toeplitz operators on the polydisc and the unit ball....................................18 4. Subspaces of weighted shifts.....................................................................23 5. Joint spectra for N-tuples of operators........................................................27 6. Algebras of operator weighted shifts...........................................................30 7. Functional calculus for N-tuples of contractions..........................................37 8. Dual algebras, invariant subspace problem and reflexivity..........................44 9. Reflexivity of jointly quasinormal operators and spherical isometries..........45 10. Reflexivity and existence of invariant subspaces......................................47 11. Questions and open problems..................................................................56 References.....................................................................................................58
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