Geodesic
Series representation of compact linear operators in Banach spaces
Commentationes Mathematicae, Tome 56 (2016) no. 1, p. 17−27.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

Let \(p\in(1,\infty)\) and \(I=(0,1)\); suppose that \(T\colon L_{p}(I)\rightarrow L_{p}(I)\) is a~compact linear map with trivial kernel and range dense in \(L_{p}(I)\). It is shown that if the Gelfand numbers of \(T\) decay sufficiently quickly, then the action of \(T\) is given by a series with calculable coefficients. The special properties of \(L_{p}(I)\) enable this to be established under weaker conditions on the Gelfand numbers than in earlier work set in the context of more general spaces.
DOI : 10.14708/cm.v56i1.1139
Classification : 15A18, 46B50, 47B38, 47A58, 47A60
Mots-clés : Eigenvalues, Banach spaces, compact operators, nuclear maps, Gelfand numbers 
@article{10_14708_cm_v56i1_1139,
     author = {David E. Edmunds and Jan Lang},
     title = {Series representation of compact linear operators in {Banach} spaces},
     journal = {Commentationes Mathematicae},
     pages = { 17\ensuremath{-}27},
     publisher = {mathdoc},
     volume = {56},
     number = {1},
     year = {2016},
     doi = {10.14708/cm.v56i1.1139},
     language = {pl},
     url = {http://geodesic.mathdoc.fr/articles/10.14708/cm.v56i1.1139/}
}
TY  - JOUR
AU  - David E. Edmunds
AU  - Jan Lang
TI  - Series representation of compact linear operators in Banach spaces
JO  - Commentationes Mathematicae
PY  - 2016
SP  -  17−27
VL  - 56
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.14708/cm.v56i1.1139/
DO  - 10.14708/cm.v56i1.1139
LA  - pl
ID  - 10_14708_cm_v56i1_1139
ER  - 
%0 Journal Article
%A David E. Edmunds
%A Jan Lang
%T Series representation of compact linear operators in Banach spaces
%J Commentationes Mathematicae
%D 2016
%P  17−27
%V 56
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.14708/cm.v56i1.1139/
%R 10.14708/cm.v56i1.1139
%G pl
%F 10_14708_cm_v56i1_1139
David E. Edmunds; Jan Lang. Series representation of compact linear operators in Banach spaces. Commentationes Mathematicae, Tome 56 (2016) no. 1, p.  17−27. doi : 10.14708/cm.v56i1.1139. http://geodesic.mathdoc.fr/articles/10.14708/cm.v56i1.1139/

Cité par Sources :