Series representation of compact linear operators in Banach spaces

David E. Edmunds, and Jan Lang. "Series representation of compact linear operators in Banach spaces." Commentationes Mathematicae 56.1 (2016): null. <http://eudml.org/doc/292498>.

@article{DavidE2016,
abstract = {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.},
author = {David E. Edmunds, Jan Lang},
journal = {Commentationes Mathematicae},
keywords = {Eigenvalues; Banach spaces; compact operators; nuclear maps; Gelfand numbers},
language = {eng},
number = {1},
pages = {null},
title = {Series representation of compact linear operators in Banach spaces},
url = {http://eudml.org/doc/292498},
volume = {56},
year = {2016},
}

TY - JOUR
AU - David E. Edmunds
AU - Jan Lang
TI - Series representation of compact linear operators in Banach spaces
JO - Commentationes Mathematicae
PY - 2016
VL - 56
IS - 1
SP - null
AB - 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.
LA - eng
KW - Eigenvalues; Banach spaces; compact operators; nuclear maps; Gelfand numbers
UR - http://eudml.org/doc/292498
ER -