Supertauberian operators and perturbations.

González, M., and Martínez-Abejón, A.. "Supertauberian operators and perturbations.." Extracta Mathematicae 8.2-3 (1993): 92-97. <http://eudml.org/doc/38387>.

@article{González1993,
abstract = {Upper semi-Fredholm operators and tauberian operators in Banach spaces admit the following perturbative characterizations [6], [2]: An operator T: X --&gt; Y is upper semi-Fredholm (tauberian) if and only if for every compact operator K: X --&gt; Y the kernel N(T+K) is finite dimensional (reflexive). In [7] Tacon introduces an intermediate class between upper semi-Fredholm operators and tauberian operators, the supertauberian operators, and he studies this class using non-standard analysis. Here we study supertauberian operators using ultrapower of Banach spaces and, among other results, we obtain a perturbative characterization. As a consequence we characterize Banach spaces in which all superreflexive subspaces are finite dimensional, and Banach spaces in which all reflexive subspaces are superreflexive. Similar results are obtained for the dual class of cosupertauberian operators, including a perturbative characterization of this class, and characterizations of Banach spaces in which all quotients are finite dimensional, and Banach spaces in which all reflexive quotients are superreflexive.},
author = {González, M., Martínez-Abejón, A.},
journal = {Extracta Mathematicae},
keywords = {Algebra de operadores; Espacios de Banach; Espacio reflexivo; Operadores de Fredholm; Teoría de perturbación; Tauberian operators; perturbative characterisation; ultrapowers of Banach spaces},
language = {eng},
number = {2-3},
pages = {92-97},
title = {Supertauberian operators and perturbations.},
url = {http://eudml.org/doc/38387},
volume = {8},
year = {1993},
}

TY - JOUR
AU - González, M.
AU - Martínez-Abejón, A.
TI - Supertauberian operators and perturbations.
JO - Extracta Mathematicae
PY - 1993
VL - 8
IS - 2-3
SP - 92
EP - 97
AB - Upper semi-Fredholm operators and tauberian operators in Banach spaces admit the following perturbative characterizations [6], [2]: An operator T: X --&gt; Y is upper semi-Fredholm (tauberian) if and only if for every compact operator K: X --&gt; Y the kernel N(T+K) is finite dimensional (reflexive). In [7] Tacon introduces an intermediate class between upper semi-Fredholm operators and tauberian operators, the supertauberian operators, and he studies this class using non-standard analysis. Here we study supertauberian operators using ultrapower of Banach spaces and, among other results, we obtain a perturbative characterization. As a consequence we characterize Banach spaces in which all superreflexive subspaces are finite dimensional, and Banach spaces in which all reflexive subspaces are superreflexive. Similar results are obtained for the dual class of cosupertauberian operators, including a perturbative characterization of this class, and characterizations of Banach spaces in which all quotients are finite dimensional, and Banach spaces in which all reflexive quotients are superreflexive.
LA - eng
KW - Algebra de operadores; Espacios de Banach; Espacio reflexivo; Operadores de Fredholm; Teoría de perturbación; Tauberian operators; perturbative characterisation; ultrapowers of Banach spaces
UR - http://eudml.org/doc/38387
ER -