Packing spheres in spaces
Paracommutators. Brief introduction, open problems.
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...
Paracommutators of Schatten- von Neumann class S..., 0 < p < 1.
Perturbation of the spectrum οf an essentially selfadjoint operator
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.
Perturbation theorems for Hermitian elements in Banach algebras
Two well-known theorems for Hermitian elements in C*-algebras are extended to Banach algebras. The first concerns the solution of the equation ax - xb = y, and the second gives sharp bounds for the distance between spectra of a and b when a, b are Hermitian.
Perturbations of real parts of eigenvalues of bounded linear operators in a Hilbert space
Let be a bounded linear operator in a complex separable Hilbert space , and be a selfadjoint operator in . Assuming that belongs to the Schatten-von Neumann ideal
Perturbations of the H∞-calculus
Suppose A is a sectorial operator on a Banach space X, which admits an H∞-calculus. We study conditions on a multiplicative perturbation B of A which ensure that B also has an H∞-calculus. We identify a class of bounded operators T : X→X, which we call strongly triangular, such that if B = (1 + T) A is sectorial then it also has an H∞-calculus. In the case X is a Hilbert space an operator is strongly triangular if and only if ∑ Sn(T)/n <∞ where (Sn(T))n=1∞ are the singular values of T.
Polar lattices from the point of view of nuclear spaces.
The aim of this survey article is to show certain questions concerning nuclear spaces and linear operators in normed spaces lead to questions from geometry of numbers.
Positive Schatten class Toeplitz operators on the ball
On the harmonic Bergman space of the ball, we give characterizations for an arbitrary positive Toeplitz operator to be a Schatten class operator in terms of averaging functions and Berezin transforms.
Positive Schatten-Herz class Toeplitz operators on the ball.
Preassigning eigenvalues and zeros of nuclear operators
p-representable operators in Banach spaces.
Probabilités cylindriques stables sur les espaces et applications du théorème de dualité
Produits tensoriels complétés d'espaces de Hilbert
Produits tensoriels et , applications -sommantes, applications -radonifiantes
Pseudocomplémentation dans les espaces de Banach
This paper introduces the following definition: a closed subspace Z of a Banach space E is pseudocomplemented in E if for every linear continuous operator u from Z to Z there is a linear continuous extension ū of u from E to E. For instance, every subspace complemented in E is pseudocomplemented in E. First, the pseudocomplemented hilbertian subspaces of are characterized and, in with p in [1, + ∞[, classes of closed subspaces in which the notions of complementation and pseudocomplementation...
p-trivial Banach spaces
Putnam-Fuglede theorem and the range-kernel orthogonality of derivations.