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1
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p-Analytic and p-quasi-analytic vectors

100%
Rusinek J.
Studia Mathematica
|
1998
|
tom 127
|
nr 3
233-250
EN
For every symmetric operator acting in a Hilbert space, we introduce the families of p-analytic and p-quasi-analytic vectors (p>0), indexed by positive numbers. We prove various properties of these families. We make use of these families to show that certain results guaranteeing essential selfadjointness of an operator with sufficiently large sets of quasi-analytic and Stieltjes vectors are optimal.
2
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Generalized Analytic and Quasi-Analytic Vectors

100%
Rusinek J.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2004
|
tom 52
|
nr 1
39-46
EN
For every sequence (aₙ) of positive real numbers and an operator acting in a Banach space, we introduce the families of (aₙ)-analytic and (aₙ)-quasi-analytic vectors. We prove various properties of these families.
3
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Pseudotopologies with applications to one-parameter groups, von Neumann algebras, and Lie algebra representations

100%
Rusinek J.
Studia Mathematica
|
1993
|
tom 107
|
nr 3
273-286
EN
For any pair E,F of pseudotopological vector spaces, we endow the space L(E,F) of all continuous linear operators from E into F with a pseudotopology such that, if G is a pseudotopological space, then the mapping L(E,F) × L(F,G) ∋ (f,g) → gf ∈ L(E,G) is continuous. We use this pseudotopology to establish a result about differentiability of certain operator-valued functions related with strongly continuous one-parameter semigroups in Banach spaces, to characterize von Neumann algebras, and to establish a result about integration of Lie algebra representations.
4
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On generalized canonical commutation relations

32%
Rusinek J.
Studia Mathematica
|
1990
|
tom 96
|
nr 2
175-181
5
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Analytic vectors and generation of one-parameter groups

32%
Rusinek J.
Studia Mathematica
|
1984
|
tom 79
|
nr 1
77-82
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