The Kreĭn-Šmul'jan theorem revisited - Gonzalez Zerbo, Santiago; Maestripieri, Alejandra; Martínez Pería, Francisco (Linear algebra and its applications, 2025)
We present a generalization of the Kreĭn-Šmul'jan theorem involving several operators: Given bounded selfadjoint operators A,B1,…,Bm acting on a Hilbert space H, we provide sufficient conditions to determine whether there are λ1,…,λm∈R such that A+∑i=1mλiBi is a positive semidefinite operator.