Lifting Hankel operators from the Hardy space to the Bergman space (Q756095)

The map \(\Phi\) of the matrix \((a_{ij})\) to \((\Phi (a_{ij})(i+1)^{1/2}(j+1)^{1/2}(i+j+1)^{-1})\) takes Hankel matrices (associated to Hankel operators on the Hardy space) to matrix realizations of Hankel operators on the Bergman space. The author develops several properties of \(\Phi\) ; e.g. \(\Phi\) is an injective contraction. Several problems and questions relted to \(\Phi\) are included.