-compact operators.
-regularized -resolvent families: regularity and local properties.
... and Schrödinger operators.
-hypercyclic and disjoint -hypercyclic properties of binary relations over topological spaces
We examine various types of -hypercyclic (-topologically transitive) and disjoint -hypercyclic (disjoint -topologically transitive) properties of binary relations over topological spaces. We pay special attention to finite structures like simple graphs, digraphs and tournaments, providing a great number of illustrative examples.
-absolutely summing operators on the space and applications.
-vectors and boundedness
The following two questions as well as their relationship are studied: (i) Is a closed linear operator in a Banach space bounded if its -vectors coincide with analytic (or semianalytic) ones? (ii) When are the domains of two successive powers of the operator in question equal? The affirmative answer to the first question is established in case of paranormal operators. All these investigations are illustrated in the context of weighted shifts.
-Spaces and cone summing operators
1-amenability of 𝒜(X) for Banach spaces with 1-unconditional bases
The main result of the note is a characterization of 1-amenability of Banach algebras of approximable operators for a class of Banach spaces with 1-unconditional bases in terms of a new basis property. It is also shown that amenability and symmetric amenability are equivalent concepts for Banach algebras of approximable operators, and that a type of Banach space that was long suspected to lack property 𝔸 has in fact the property. Some further ideas on the problem of whether or not amenability (in...
1D dirac operators with special periodic potentials
2-local Jordan automorphisms on operator algebras
We investigate 2-local Jordan automorphisms on operator algebras. In particular, we show that every 2-local Jordan automorphism of the algebra of all n× n real or complex matrices is either an automorphism or an anti-automorphism. The same is true for 2-local Jordan automorphisms of any subalgebra of ℬ which contains the ideal of all compact operators on X, where X is a real or complex separable Banach spaces and ℬ is the algebra of all bounded linear operators on X.
2-local Lie isomorphisms of operator algebras on Banach spaces
Let X and Y be complex Banach spaces of dimension greater than 2. We show that every 2-local Lie isomorphism ϕ of B(X) onto B(Y) has the form ϕ = φ + τ, where φ is an isomorphism or the negative of an anti-isomorphism of B(X) onto B(Y), and τ is a homogeneous map from B(X) into ℂI vanishing on all finite sums of commutators.
2-magnon scattering in the Heisenberg model
2-summing multiplication operators
Let 1 ≤ p < ∞, be a sequence of Banach spaces and the coresponding vector valued sequence space. Let , be two sequences of Banach spaces, , Vₙ: Xₙ → Yₙ, a sequence of bounded linear operators and 1 ≤ p,q < ∞. We define the multiplication operator by . We give necessary and sufficient conditions for to be 2-summing when (p,q) is one of the couples (1,2), (2,1), (2,2), (1,1), (p,1), (p,2), (2,p), (1,p), (p,q); in the last case 1 < p < 2, 1 < q < ∞.
3 Classification des plongements isotropes d'après A. Weinstein
*-algebras of unbounded operators affiliated with a von Neumann algebra.
(Conférence n°1) Applications -sommantes, pour réel , et démonstration d’une conjecture de Pietsch
(Conférence n°1) Applications -sommantes, pour réel , et démonstration d’une conjecture de Pietsch
(Conférence n°2) Une propriété caractéristique des processus linéaires continus. Applications aux opérateurs -radonifiants
(Conférence n°2) Une propriété caractéristique des processus linéaires continus. Applications aux opérateurs -radonifiants
(E,F)-Schur multipliers and applications
For two given symmetric sequence spaces E and F we study the (E,F)-multiplier space, that is, the space of all matrices M for which the Schur product M ∗ A maps E into F boundedly whenever A does. We obtain several results asserting continuous embedding of the (E,F)-multiplier space into the classical (p,q)-multiplier space (that is, when , ). Furthermore, we present many examples of symmetric sequence spaces E and F whose projective and injective tensor products are not isomorphic to any subspace...