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1
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Decomposition and disintegration of positive definite kernels on convex *-semigroups

100%
Stochel J.
Annales Polonici Mathematici
|
1991-1992
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tom 56
|
nr 3
243-294
EN
Contents Introduction. 1. Preliminaries. 2. Predilatable kernels. 3. Criteria of predilatability. 4. Degenerate and nondegenerate predilatable kernels. 5. Canonical decomposition of predilatable kernels. 6. Weakly predilatable kernels. 7. Disintegration of nondegenerate predilatable kernels. 8. Continuity of predilatable mappings on topological *-algebras. 9. Disintegration of holomorphic positive definite mappings on commutative Banach *-algebras. 10. Holomorphic positive definite mappings on noncommutative Banach *-algebras. 11. Completely positive k-linear mappings. 12. Multiplicative k-homogeneous polynomials. 13. Positive definiteness versus complete positivity. 14. Appendix References.
2
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Logarithmic concavity, unitarity and selfadjointness

100%
Stochel J.
Banach Center Publications
|
2005
|
tom 67
|
nr 1
335-348
EN
Isometric automorphisms of normed linear spaces are characterized by suitable concavity properties of powers of operators. Bounded selfadjoint operators in Hilbert spaces are described by parallel concavity properties of the exponential group. Unbounded infinitesimal generators of 𝓒₀-groups of Hilbert space operators having concavity properties are characterized as well.
3
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$𝒞^∞$-vectors and boundedness

64%
Stochel J., Szafraniec F.
Annales Polonici Mathematici
|
1997
|
tom 66
|
nr 1
223-238
EN
The following two questions as well as their relationship are studied: (i) Is a closed linear operator in a Banach space bounded if its $𝒞^∞$-vectors coincide with analytic (or semianalytic) ones? (ii) When are the domains of two successive powers of the operator in question equal? The affirmative answer to the first question is established in case of paranormal operators. All these investigations are illustrated in the context of weighted shifts.
4
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Joint subnormality of n-tuples and C₀-semigroups of composition operators on L²-spaces, II

64%
Budzyński P., Stochel J.
Studia Mathematica
|
2009
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tom 193
|
nr 1
29-52
EN
In the previous paper, we have characterized (joint) subnormality of a C₀-semigroup of composition operators on L²-space by positive definiteness of the Radon-Nikodym derivatives attached to it at each rational point. In the present paper, we show that in the case of C₀-groups of composition operators on L²-space the positive definiteness requirement can be replaced by a kind of consistency condition which seems to be simpler to work with. It turns out that the consistency condition also characterizes subnormality of C₀-semigroups of composition operators on L²-space induced by injective and bimeasurable transformations. The consistency condition, when formulated in the language of the Laplace transform, takes a multiplicative form. The paper concludes with some examples.
5
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Selfadjoint operator matrices with finite rows

64%
Janas J., Stochel J.
Annales Polonici Mathematici
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1997
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tom 66
|
nr 1
155-172
EN
A generalization of the Carleman criterion for selfadjointness of Jacobi matrices to the case of symmetric matrices with finite rows is established. In particular, a new proof of the Carleman criterion is found. An extension of Jørgensen's criterion for selfadjointness of symmetric operators with "almost invariant" subspaces is obtained. Some applications to hyponormal weighted shifts are given.
6
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Joint subnormality of n-tuples and C₀-semigroups of composition operators on L²-spaces

64%
Budzyński P., Stochel J.
Studia Mathematica
|
2007
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tom 179
|
nr 2
167-184
EN
Joint subnormality of a family of composition operators on L²-space is characterized by means of positive definiteness of appropriate Radon-Nikodym derivatives. Next, simplified positive definiteness conditions guaranteeing joint subnormality of a C₀-semigroup of composition operators are supplied. Finally, the Radon-Nikodym derivatives associated to a jointly subnormal C₀-semigroup of composition operators are shown to be the Laplace transforms of probability measures (modulo a C₀-group of scalars) constituting a measurable family.
7
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Backward extensions of hyperexpansive operators

52%
Jabłoński Z., Jung I., Stochel J.
Studia Mathematica
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2006
|
tom 173
|
nr 3
233-257
EN
The concept of k-step full backward extension for subnormal operators is adapted to the context of completely hyperexpansive operators. The question of existence of k-step full backward extension is solved within this class of operators with the help of an operator version of the Levy-Khinchin formula. Some new phenomena in comparison with subnormal operators are found and related classes of operators are discussed as well.
8
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Operators with absolute continuity properties: an application to quasinormality

52%
Jabłoński Z., Jung I., Stochel J.
Studia Mathematica
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2013
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tom 215
|
nr 1
11-30
EN
An absolute continuity approach to quasinormality which relates the operator in question to the spectral measure of its modulus is developed. Algebraic characterizations of some classes of operators that emerge in this context are found. Various examples and counterexamples illustrating the concepts of the paper are constructed by using weighted shifts on directed trees. Generalizations of these results that cover the case of q-quasinormal operators are established.
9
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On a binary relation between normal operators

52%
Okayasu T., Stochel J., Ueda Y.
Studia Mathematica
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2011
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tom 204
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nr 3
247-264
EN
The main goal of this paper is to clarify the antisymmetric nature of a binary relation ≪ which is defined for normal operators A and B by: A ≪ B if there exists an operator T such that $E_{A}(Δ) ≤ T*E_{B}(Δ)T$ for all Borel subset Δ of the complex plane ℂ, where $E_{A}$ and $E_{B}$ are spectral measures of A and B, respectively (the operators A and B are allowed to act in different complex Hilbert spaces). It is proved that if A ≪ B and B ≪ A, then A and B are unitarily equivalent, which shows that the relation ≪ is a partial order modulo unitary equivalence.
10
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On the Sz.-Nagy boundedness condition on abelian involution semigroups

44%
Stochel J.
Colloquium Mathematicum
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1987
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tom 54
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nr 2
267-271
11

The Bochner-Kolmogorov extension theorem for semispectral measures

44%
Stochel J.
Colloquium Mathematicum
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1987
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tom 54
|
nr 1
83-94
12
Content available remote

Characterizations of subnormal operators

26%
Stochel J.
Studia Mathematica
|
1990
|
tom 97
|
nr 3
227-238
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