On the Cesàro operator in weighted \(l^{2}\)-sequence spaces and the generalized concept of normality (Q1947154)

In the paper under review, the author examines the question which symbol \(h\) induces a hyponormal (i.e., self-commtator is positive semi-definite) weighted Cesàro operator \(C_h\) in a weighted \(\ell^2\)-space \(\ell^2(h)\). The author offers explicit necessary and sufficient conditions for hyponormality of \(C_h\) in terms of the symbol \(h\). Moreover, she shows that the weighted Cesàro operator is never quasinormal (i.e., \(C_h\) commutes with \(C_h^*C_h\)).