Connectivity of level sets of quadratic forms and Hausdorff-Toeplitz type theorems
Given an arbitrary operator \(A: X\to X\) in a complex pre-Hilbert space \(X\), \(\dim X\geq 3\), the authors prove that all level sets \(F(A,\lambda)= \{x\in X:\langle Ax,x\rangle= \lambda\), \(|x|= 1\}\) are connected. Related to this main result, many other ones are derived by specializing \(A\) and \(F(A,\lambda)\).
scientific article; zbMATH DE number 1121757