-compact 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
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-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 < ∞.
(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...
-partitions of unity on normed spaces
(Nonsymmetric) Dirichlet operators on : existence, uniqueness and associated Markov processes
ℱ-singular and G-cosingular operators
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The aim is to investigate certain spectral properties, such as decomposability, the spectral mapping property and the Lyubich-Matsaev property, for linear differential operators with constant coefficients ( and more general Fourier multiplier operators) acting in . The criteria developed for such operators are quite general and p-dependent, i.e. they hold for a range of p in an interval about 2 (which is typically not (1,∞)). The main idea is to construct appropriate functional calculi: this is...
(Weakly) Compact Mappings into (F)-Spaces:
"Zero-two'' law for conservative Markov operators