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arXiv · 2507.17525

Krein-Šmul'jan Theorem Revisited

Santiago gonzalez Zerbo·Alejandra Maestripieri·Francisco Martínez Pería
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Abstract

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

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Santiago gonzalez Zerbo, Alejandra Maestripieri, Francisco Martínez Pería. 2025-07-23. Krein-Šmul'jan Theorem Revisited. https://arxiv.org/abs/2507.17525

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