In order to study the absolute summability of an operator T we consider the set ST = {{xn} | ∑||Txn|| < ∞}. It is well known that an operator T in a Hilbert space is nuclear if and only if ST contains an orthonormal basis and it is natural to ask under which conditions two orthonormal basis define the same left ideal of nuclear operators. Using results about ST we solve this problem in the more general context of Banach spaces.
@article{urn:eudml:doc:38941,
title = {Some results about absolute summability of operators in Banach spaces.},
journal = {Stochastica},
volume = {10},
year = {1986},
pages = {5-11},
zbl = {0629.47019},
mrnumber = {MR0885058},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:38941}
}
López Corral, Luis. Some results about absolute summability of operators in Banach spaces.. Stochastica, Tome 10 (1986) pp. 5-11. http://gdmltest.u-ga.fr/item/urn:eudml:doc:38941/