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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.

Paracommutators. Brief introduction, open problems.

Jaak Peetre (1989)

Revista Matemática de la Universidad Complutense de Madrid

We review the basic facts about the theory of paracommutators in Rn (sec S. Janson, J. Peetre, Trans. Am. Math. Soc. 305 (1988), 467504). We also give an interpretation of paracommutators from the point of view of group representations. This suggests a generalization to more general groups. Here we sketch a theory of paracommutators over stratified groups. This include the famous Heisenberg group. Finally, we take up the question of generalizing the notion of Schatten-von Neumann trace ideals to...

Partial differential equations in Banach spaces involving nilpotent linear operators

Antonia Chinnì, Paolo Cubiotti (1996)

Annales Polonici Mathematici

Let E be a Banach space. We consider a Cauchy problem of the type ⎧ D t k u + ∑ j = 0 k - 1 ∑ | α | ≤ m A j , α ( D t j D x α u ) = f in ℝ n + 1 , ⎨ ⎩ D t j u ( 0 , x ) = φ j ( x ) in ℝ n , j=0,...,k-1, where each A j , α is a given continuous linear operator from E into itself. We prove that if the operators A j , α are nilpotent and pairwise commuting, then the problem is well-posed in the space of all functions u ∈ C ∞ ( ℝ n + 1 , E ) whose derivatives are equi-bounded on each bounded subset of ℝ n + 1 .

Partially defined σ-derivations on semisimple Banach algebras

Tsiu-Kwen Lee, Cheng-Kai Liu (2009)

Studia Mathematica

Let A be a semisimple Banach algebra with a linear automorphism σ and let δ: I → A be a σ-derivation, where I is an ideal of A. Then Φ(δ)(I ∩ σ(I)) = 0, where Φ(δ) is the separating space of δ. As a consequence, if I is an essential ideal then the σ-derivation δ is closable. In a prime C*-algebra, we show that every σ-derivation defined on a nonzero ideal is continuous. Finally, any linear map on a prime semisimple Banach algebra with nontrivial idempotents is continuous if it satisfies the σ-derivation...

Perturbation of the spectrum οf an essentially selfadjoint operator

Andrzej Pokrzywa (1993)

Applicationes Mathematicae

The aim of this paper is to find estimates of the Hausdorff distance between the spectra of two nonselfadjoint operators. The operators considered are assumed to have their imaginary parts in some normed ideal of compact operators. In the case of the classical Schatten ideals the estimates are given explicitly.

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