Operadores sobre espacios de sucesiones infraperiódicas con valores vectoriales (II).
Opérateurs convexifiants
Opérateurs de Toeplitz de plusieurs variables complexes
Opérateurs diagonaux dans les espaces à bases.
Opérateurs dissipatifs et codissipatifs invariants par translations sur les groupes localement compacts
Opérateurs dissipatifs et semi-groupes dans les espaces de fonctions continues
Soit un espace localement compact. Tout opérateur dissipatif de domaine dense dans est limite d’opérateurs dissipatifs bornés. Ce résultat permet, dans le cas où est un espace homogène, de démontrer que tout opérateur dissipatif, de domaine dense et invariant sur se prolonge en le générateur infinitésimal d’un semi-groupe à contraction invariant sur .À tout opérateur vérifiant le principe du maximum positif sur et de domaine assez riche, on associe un opérateur bilinéaire , appelé...
Opérateurs extrémaux dans certains espaces de Banach
Opérateurs intégraux de Fourier d'ordre infini sur les espaces de Gevrey. Applications au problème de Cauchy pour des opérateurs hyperboliques
Opérateurs réguliers sur les espaces
Opérateurs se factorisant par un espace , d’après S. Kwapien (suite et fin)
Opérateurs se factorisant par un espace , d’après S. Kwapien
Opérateurs sommants et factorisations. A travers les espaces
Opérateurs sommants sur un cone normal d un espace de Banach.
The aim of this paper is to develop a theory of p-summing operators (between Banach spaces) in presence of an order structure given by a convex normal cone.
Opérateurs sur un espace
Opérateurs uniformément convexifiants
Operational quantities derived from the norm and generalized Fredholm theory
We introduce and study some operational quantities associated to a space ideal . These quantities are used to define generalized semi-Fredholm operators associated to , and the corresponding perturbation classes which extend the strictly singular and strictly cosingular operators, and we study the generalized Fredholm theory obtained in this way. Finally we present some examples and show that the classes of generalized semi-Fredholm operators are non-trivial for several classical space ideals.
Operator equations and subscalarity
We consider the system of operator equations ABA = A² and BAB = B². Let (A,B) be a solution to this system. We give several connections among the operators A, B, AB, and BA. We first prove that A is subscalar of finite order if and only if B is, which is equivalent to the subscalarity of AB or BA with finite order. As a corollary, if A is subscalar and its spectrum has nonempty interior, then B has a nontrivial invariant subspace. We also provide examples of subscalar operator matrices. Moreover,...
Operator fractional-linear transformations: convexity and compactness of image; applications
The present paper consists of two parts. In Section 1 we consider fractional-linear transformations (f.-l.t. for brevity) F in the space of all linear bounded operators acting from into , where are Banach spaces. We show that in the case of Hilbert spaces the image F(ℬ) of any (open or closed) ball ℬ ⊂ D(F) is convex, and if ℬ is closed, then F(ℬ) is compact in the weak operator topology (w.o.t.) (Theorem 1.2). These results extend the corresponding results on compactness obtained in [3],...
Operator ideal properties of vector measures with finite variation
Given a vector measure m with values in a Banach space X, a desirable property (when available) of the associated Banach function space L¹(m) of all m-integrable functions is that L¹(m) = L¹(|m|), where |m| is the [0,∞]-valued variation measure of m. Closely connected to m is its X-valued integration map Iₘ: f ↦ ∫f dm for f ∈ L¹(m). Many traditional operators from analysis arise as integration maps in this way. A detailed study is made of the connection between the property L¹(m) = L¹(|m|) and the...
Operator Lipschitz functions on Banach spaces
Let X, Y be Banach spaces and let (X,Y) be the space of bounded linear operators from X to Y. We develop the theory of double operator integrals on (X,Y) and apply this theory to obtain commutator estimates of the form for a large class of functions f, where A ∈ (X), B ∈ (Y) are scalar type operators and S ∈ (X,Y). In particular, we establish this estimate for f(t): = |t| and for diagonalizable operators on and for p < q. We also study the estimate above in the setting of Banach ideals...