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.
@article{bwmeta1.element.bwnjournal-article-doi-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},
volume = {215},
year = {2013},
pages = {265-278},
zbl = {1277.47027},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-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 215 (2013) pp. 265-278. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm214-3-5/