Martín Peinador, Elena2023-06-202023-06-201990-12-030003-889X10.1007/BF01191694https://hdl.handle.net/20.500.14352/58565It is a well known fact that operators on a separable Hilbert space H giving norm-summability on an orthonormal basis have to be nuclear (Holub 1972) and operators giving summability on an orthonormal basis must be Hilbert-Schmidt. In former papers the author characterizes all the sequences of H that in this respect behave as orthonormal basis, and in the present paper those results are in some way, generalized to a separable Banach space.engjournal articlehttp://link.springer.com/article/10.1007%2FBF01191694#http://link.springer.comrestricted access517.98Compact operatornuclear operatorabsolutely summable sequencenorm-summability on an orthonormal basisHilbert-SchmidtTopología1210 Topología