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1
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The algebra generated by a pair of operator weighted shifts

100%
Ptak M.
Annales Polonici Mathematici
|
1995
|
tom 62
|
nr 2
97-110
EN
We present a model for two doubly commuting operator weighted shifts. We also investigate general pairs of operator weighted shifts. The above model generalizes the model for two doubly commuting shifts. WOT-closed algebras for such pairs are described. We also deal with reflexivity for such pairs assuming invertibility of operator weights and a condition on the joint point spectrum.
2
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On the reflexivity and hyperreflexivity of algebras and subspaces

100%
Ptak M.
Banach Center Publications
|
2007
|
tom 75
|
nr 1
249-259
EN
A review of recent reflexivity and hyperreflexivity results is presented. We concentrate particularly on a finite-dimensional situation, Toeplitz operators and partial isometries. Open problems in this area are given.
3
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Erratum to the paper "On the reflexivity of pairs of isometries and of tensor products of some reflexive algebras" (Studia Math. 83 (1986), 47-55)

100%
Ptak M.
Studia Mathematica
|
1992
|
tom 103
|
nr 2
221-223
EN
A gap in the proof of [4, Theorem 1] is removed.
4
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Continuous isometric semigroups and reflexivity

100%
Ptak M.
Annales Polonici Mathematici
|
1991
|
tom 54
|
nr 1
21-28
EN
 Abstract. We consider the reflexivity of a WOT-closed algebra generated by continuous isometric semigroups parametrized by the semigroup of non-negative reals or the semigroup of finite sequences of non-negative reals. It is also proved that semigroups of continuous unilateral multi-parameter shifts are reflexive.
5
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Projections onto the spaces of Toeplitz operators

100%
Ptak M.
Annales Polonici Mathematici
|
2005
|
tom 86
|
nr 2
97-105
EN
Projections onto the spaces of all Toeplitz operators on the N-torus and the unit sphere are constructed. The constructions are also extended to generalized Toeplitz operators and applied to show hyperreflexivity results.
6
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Reflexivity of Toeplitz operators in multiply connected regions

64%
Młocek W., Ptak M.
Colloquium Mathematicum
|
2016
|
tom 142
|
nr 1
83-97
EN
Subspaces of Toeplitz operators on the Hardy spaces over a multiply connected region in the complex plane are investigated. A universal covering map of such a region and the group of automorphisms invariant with respect to the covering map connect the Hardy space on this multiply connected region with a certain subspace of the classical Hardy space on the disc. We also present some connections of Toeplitz operators on both spaces from the reflexivity point of view.
7
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Properties of two variables Toeplitz type operators

64%
Król-Klimkowska E., Ptak M.
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
|
2016
|
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.
8
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Quasinormal operators are hyperreflexive

64%
Kliś K., Ptak M.
Banach Center Publications
|
2005
|
tom 67
|
nr 1
241-244
EN
We will prove the statement in the title. We also give a better estimate for the hyperreflexivity constant for an analytic Toeplitz operator.
9
Content available remote

On the reflexivity of pairs of isometries and of tensor products of some operator algebras

44%
Ptak M.
Studia Mathematica
|
1986
|
tom 83
|
nr 1
57-95
10
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
Content available

Unitary dilations of multi-parameter semigroups of operators

44%
Ptak M.
Annales Polonici Mathematici
|
1985
|
tom 45
|
nr 3
237-243
11
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Unitary dilation and fixed point theorem

38%
Ptak M.
Annales Polonici Mathematici
|
1989-1990
|
tom 50
|
nr 2
153-155
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