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1
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Reinsurance-a new approach

100%
Paszkiewicz A., Olejnik J.
Banach Center Publications
|
2010
|
tom 90
|
nr 1
139-151
EN
We describe a new model of multiple reinsurance. The main idea is that the reinsurance premium is paid conditionally. It is motivated by some analysis of the ultimate price of the reinsurance contract. For simplicity we assume that the underlying risk pricing functional is the L₂-norm. An unexpected relation to the general theory of sample regularity of stochastic processes is given.
2
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Almost sure approximation of unbounded operators in $L_2 (X,A,μ)$

100%
Jajte R., Paszkiewicz A.
Studia Mathematica
|
1998
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tom 128
|
nr 2
103-120
EN
The possibilities of almost sure approximation of unbounded operators in $L_2(X,A,μ)$ by multiples of projections or unitary operators are examined.
3
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Convergence of orthogonal series of projections in Banach spaces

100%
Jajte R., Paszkiewicz A.
Annales Polonici Mathematici
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1997
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tom 66
|
nr 1
137-153
EN
For a sequence $(A_j)$ of mutually orthogonal projections in a Banach space, we discuss all possible limits of the sums $S_n = ∑^n_{j=1} A_j$ in a "strong" sense. Those limits turn out to be some special idempotent operators (unbounded, in general). In the case of X = L₂(Ω,μ), an arbitrary unbounded closed and densely defined operator A in X may be the μ-almost sure limit of $S_n$ (i.e. $S_{n}f → Af$ μ-a.e. for all f ∈ 𝓓(A)).
4
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The bundle convergence in von Neumann algebras and their $L_2$-spaces

81%
Hensz E., Jajte R., Paszkiewicz A.
Studia Mathematica
|
1996
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tom 120
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nr 1
23-46
EN
A stronger version of almost uniform convergence in von Neumann algebras is introduced. This "bundle convergence" is additive and the limit is unique. Some extensions of classical limit theorems are obtained.
5
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Dilation theorems for completely positive maps and map-valued measures

81%
Hensz-Chądzyńska E., Jajte R., Paszkiewicz A.
Banach Center Publications
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1998
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tom 43
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nr 1
231-239
EN
The Stinespring theorem is reformulated in terms of conditional expectations in a von Neumann algebra. A generalisation for map-valued measures is obtained.
6
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The unconditional pointwise convergence of orthogonal seriesin $L_2$ over a von Neumann algebra

81%
Hensz E., Jajte R., Paszkiewicz A.
Colloquium Mathematicum
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1996
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tom 69
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nr 2
167-178
EN
The paper is devoted to some problems concerning a convergence of pointwise type in the $L_2$-space over a von Neumann algebra M with a faithful normal state Φ [3]. Here $L_2 = L_2(M,Φ)$ is the completion of M under the norm $x → |x|^2 = Φ(x*x)^{1/2}$.
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