Series representation of compact linear operators in Banach spaces
Commentationes Mathematicae, Tome 56 (2016) no. 1.
Voir la notice de l'article dans European Digital Mathematics Library
Let
p
∈
(
1
,
∞
)
and
I
=
(
0
,
1
)
; suppose that
T
:
L
p
(
I
)
→
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.
Mots-clés :
Eigenvalues, Banach spaces, compact operators, nuclear maps, Gelfand numbers
@article{COMA_2016__56_1_292498,
author = {David E. Edmunds and Jan Lang},
title = {Series representation of compact linear operators in {Banach} spaces},
journal = {Commentationes Mathematicae},
publisher = {mathdoc},
volume = {56},
number = {1},
year = {2016},
language = {en},
url = {https://geodesic-test.mathdoc.fr/item/COMA_2016__56_1_292498/}
}
David E. Edmunds; Jan Lang. Series representation of compact linear operators in Banach spaces. Commentationes Mathematicae, Tome 56 (2016) no. 1. https://geodesic-test.mathdoc.fr/item/COMA_2016__56_1_292498/