Abstract
Properties of space of diagonal operators on semi-normalized Schauder bases are studied. A necessary and sufficient condition is given for the containment of \(c_0\) in the space of compact diagonal operators on a semi-normalized Schauder basis. Using this condition it is shown that there exist semi-normalized Schauder bases of reflexive Banach spaces such that \(c_0\) does not embed in the space of compact diagonal operators on these Schauder bases.
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