Some results about absolute summability of operators in Banach spaces.
In order to study the absolute summability of an operator T we consider the set S = {{x} | ∑||Tx|| < ∞}. It is well known that an operator T in a Hilbert space is nuclear if and only if S 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 S we solve this problem in the more general context of Banach spaces.