Geodesic
Explicit representation of compact linear operators in Banach spaces via polar sets
David E. Edmunds1 ; Jan Lang2
1 Department of Mathematics University of Sussex Pevensey I Brighton, BN1 9QH, United Kingdom
2 Department of Mathematics The Ohio State University 100 Math Tower 231 West 18th Avenue Columbus, OH 43210-1174, U.S.A.
Studia Mathematica, Tome 214 (2013) no. 3, pp. 265-278 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

We consider a compact linear map $T$ acting between Banach spaces both of which are uniformly convex and uniformly smooth; it is supposed that $T$ has trivial kernel and range dense in the target space. 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. This provides a Banach space version of the well-known Hilbert space result of E. Schmidt.
DOI : 10.4064/sm214-3-5
Keywords: consider compact linear map acting between banach spaces which uniformly convex uniformly smooth supposed has trivial kernel range dense target space shown gelfand numbers decay sufficiently quickly action given series calculable coefficients provides banach space version well known hilbert space result schmidt

David E. Edmunds 1 ; Jan Lang 2

1 Department of Mathematics University of Sussex Pevensey I Brighton, BN1 9QH, United Kingdom
2 Department of Mathematics The Ohio State University 100 Math Tower 231 West 18th Avenue Columbus, OH 43210-1174, U.S.A. 
@article{10_4064_sm214_3_5,
     author = {David E. Edmunds and Jan Lang},
     title = {Explicit representation of compact linear operators
 in {Banach} spaces via polar sets},
     journal = {Studia Mathematica},
     pages = {265--278},
     year = {2013},
     volume = {214},
     number = {3},
     doi = {10.4064/sm214-3-5},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/sm214-3-5/}
}
TY  - JOUR
AU  - David E. Edmunds
AU  - Jan Lang
TI  - Explicit representation of compact linear operators
 in Banach spaces via polar sets
JO  - Studia Mathematica
PY  - 2013
SP  - 265
EP  - 278
VL  - 214
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4064/sm214-3-5/
DO  - 10.4064/sm214-3-5
LA  - en
ID  - 10_4064_sm214_3_5
ER  - 
%0 Journal Article
%A David E. Edmunds
%A Jan Lang
%T Explicit representation of compact linear operators
 in Banach spaces via polar sets
%J Studia Mathematica
%D 2013
%P 265-278
%V 214
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4064/sm214-3-5/
%R 10.4064/sm214-3-5
%G en
%F 10_4064_sm214_3_5
David E. Edmunds; Jan Lang. Explicit representation of compact linear operators
 in Banach spaces via polar sets. Studia Mathematica, Tome 214 (2013) no. 3, pp. 265-278. doi: 10.4064/sm214-3-5

Cité par Sources :