The Kreĭn-Šmul'jan theorem revisited

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....

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Vydané v:Linear algebra and its applications Ročník 727; s. 163 - 177
Hlavní autori: Gonzalez Zerbo, Santiago, Maestripieri, Alejandra, Martínez Pería, Francisco
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier Inc 15.12.2025
Predmet:
Linear operator inequalities
Quadratically constrained quadratic programming
secondary
Linear operator inequalities
Quadratically constrained quadratic programming
primary
ISSN:0024-3795
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Popis
Shrnutí: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.
ISSN:0024-3795
DOI:10.1016/j.laa.2025.08.006