Counterexample to a question on the operator equation \(T(H^{1/n}T)^ n=K\)
The authors consider the equation \(T(H^{1/n} T)^ n=K\) with some natural number \(n\) and \(H\), \(K\) being positive operators on a Hilbert space (\(H\) is nonsingular). The purpose of the paper is to show that the existence of the solution \(T\) to this equation for some number \(m>0\) need not provide the solvability of the equation for any natural \(n<m\). The results continue previous investigations of the authors.
scientific article; zbMATH DE number 166222