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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Bibliographic Details
Published in:Linear algebra and its applications Vol. 727; pp. 163 - 177
Main Authors: Gonzalez Zerbo, Santiago, Maestripieri, Alejandra, Martínez Pería, Francisco
Format: Journal Article
Language:English
Published: Elsevier Inc 15.12.2025
Subjects:
Linear operator inequalities
Quadratically constrained quadratic programming
secondary
Linear operator inequalities
Quadratically constrained quadratic programming
primary
ISSN:0024-3795
Online Access:Get full text
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Summary: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