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

David E. Edmunds, and Jan Lang. "Explicit representation of compact linear operators in Banach spaces via polar sets." Studia Mathematica 214.3 (2013): 265-278. <http://eudml.org/doc/285852>.

@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 -