Explicit representation of compact linear operators in Banach spaces via polar sets

@article{DavidE2013,
abstract = {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.},
author = {David E. Edmunds, Jan Lang},
journal = {Studia Mathematica},
keywords = {eigenvalues; Banach spaces; compact operators; nuclear maps; Gelfand numbers},
language = {eng},
number = {3},
pages = {265-278},
title = {Explicit representation of compact linear operators in Banach spaces via polar sets},
url = {http://eudml.org/doc/285852},
volume = {214},
year = {2013},
}

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
VL - 214
IS - 3
SP - 265
EP - 278
AB - 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.
LA - eng
KW - eigenvalues; Banach spaces; compact operators; nuclear maps; Gelfand numbers
UR - http://eudml.org/doc/285852
ER -