Schauder Bases and Operator Theory
  In this paper, we firstly give a matrix approach to the bases of a separable Hilbert space and then correct a mistake appearing in both review and the English translation of the Olevskii's paper. After this, we show that even a diagonal compact operator may map an orthonormal basis into a conditional basis. 
Yang Cao, Geng Tian, Bingzhe Hou
math.FA