Krein-Å mul'jan Theorem Revisited

Abstract

We present a generalization of Krein-Å mul'jan theorem which involves several operators. Given bounded selfadjoint operators $A,B_1,\dots ,B_m$ acting on a Hilbert space $\mathcal{H}$, we provide sufficient conditions to determine whether there are $\hat{I}{»}_1,\dots ,\hat{I}{»}_m\in \mathbb{R}$ such that $A+{\sum }_{i=1}^m\hat{I}{»}_i{B}_i$ is a positive semidefinite operator.

11 pages. Comments are welcomed!