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C0-Fredholm operators (IV).

Hari Bercovici (1990)

Publicacions Matemàtiques

The purpose of this paper is to develop, in the context of operators of class C0, a theory of Fredholm complexes analogous to that in [6], including an index stability result under perturbations. As a by-product, a simple proof of the additivity of the index for C0-Fredholm operators will be given.

Calcul fonctionnel dépendant de la croissance des coefficients spectraux

T. H. Nguyen (1977)

Annales de l'institut Fourier

Soient a 1 , ... , a n des éléments d’une b -algèbre commutative unifère A . On définit et étudie un “spectre” de a = ( a 1 , ... , a n ) qui dépend de la croissance des fonctions u 1 ( s ) , ... , u n ( s ) de l’égalité spectrale ( a 1 - s 1 ) u 1 ( s ) + + ( a n - s n ) u n ( s ) = 1 près du spectre simultané. À partir des propriétés de ce spectre, on construit un calcul fonctionnel qui, réduit au cas banachique, s’étend à certaines fonctions supposées seulement holomorphes à l’intérieur du spectre simultané. Ce calcul fonctionnel permet aussi d’étudier la régularité des éléments a 1 , ... , a n et des fonctions u 1 ( s ) , ... , u n ( s ) .

Calcul fonctionnel précisé pour des opérateurs elliptiques complexes en dimension un (et applications à certaines équations elliptiques complexes en dimension deux)

Pascal Auscher, Philippe Tchamitchian (1995)

Annales de l'institut Fourier

Dans cet article, on considère les opérateurs différentiels T = b ( x ) D ( a ( x ) D ) , où a ( x ) et b ( x ) sont deux fonctions mesurables, bornées et accrétives, et D = - i d d x . Les résultats principaux portent sur les propriétés fonctionnelles de T , de sa racine carrée, avec applications à l’équation elliptique t 2 u - T u = 0 sur × [ 0 , + [ . On démontre que T 1 / 2 D - 1 est un opérateur de Calderón-Zygmund qui dépend analytiquement du couple ( a , b ) . Les estimations ponctuelles optimales sur le noyau du semi-groupe exp ( - t L 1 / 2 ) et le calcul fonctionnel permettent de développer une théorie...

Calkin algebras for Banach spaces with finitely decomposable quotients

Manuel González, José M. Herrera (2003)

Studia Mathematica

For a Banach space X such that all quotients only admit direct decompositions with a number of summands smaller than or equal to n, we show that every operator T on X can be identified with an n × n scalar matrix modulo the strictly cosingular operators SC(X). More precisely, we obtain an algebra isomorphism from the Calkin algebra L(X)/SC(X) onto a subalgebra of the algebra of n × n scalar matrices which is triangularizable when X is indecomposable. From this fact we get some information on the...

Chain-finite operators and locally chain-finite operators.

Teresa Bermúdez, Antonio Martinón (1999)

Extracta Mathematicae

The problem we are concerned with in this research announcement is the algebraic characterization of chain-finite operators (global case) and of locally chain-finite operators (local case).

Characterisations of open multivalued linear operators

T. Álvarez (2006)

Studia Mathematica

The class of all open linear relations is characterised in terms of the restrictions of the linear relations to finite-codimensional subspaces. As an application, we establish two results, the first of which shows that an upper semi-Fredholm linear relation retains its index under finite rank perturbations, and the second is a density theorem for lower bounded linear relations that have closed range. Results of Labuschagne and of Mbekhta about linear operators are covered.

Characterization of Bessel sequences.

M. Laura Arias, Gustavo Corach, Miriam Pacheco (2007)

Extracta Mathematicae

Let H be a separable Hilbert space, L(H) be the algebra of all bounded linear operators of H and Bess(H) be the set of all Bessel sequences of H. Fixed an orthonormal basis E = {ek}k∈N of H, a bijection αE: Bess(H) → L(H) can be defined. The aim of this paper is to characterize α-1E (A) for different classes of operators A ⊆ L(H). In particular, we characterize the Bessel sequences associated to injective operators, compact operators and Schatten p-classes.

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