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Pseudotopologies with applications to one-parameter groups, von Neumann algebras, and Lie algebra representations

Jan Rusinek — 1993

Studia Mathematica

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...

p-Analytic and p-quasi-analytic vectors

Jan Rusinek — 1998

Studia Mathematica

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.

Generalized Analytic and Quasi-Analytic Vectors

Jan Rusinek — 2004

Bulletin of the Polish Academy of Sciences. Mathematics

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.

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