The Kreĭn-Šmul'jan theorem revisited

Abstract

We present a generalization of the Kreĭn-Šmul'jan theorem which involves several operators. Given bounded selfadjoint operators A,B_1,...,B_m acting on a Hilbert space H, we provide sufficient conditions to determine whether there are λ_1, ... , λ_m ∈ R such that A + ∑_{i=1}^m λ_i B_i is a positive semidefinite operator.