# Article

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Keywords:
commuting operators; positive selfadjoint operator; spectral representation
Summary:
Let ${\mathcal{B}}({\mathcal{H}})$ be the set of all bounded linear operators acting in Hilbert space ${\mathcal{H}}$ and ${\mathcal{B}}^{+}({\mathcal{H}})$ the set of all positive selfadjoint elements of ${\mathcal{B}}({\mathcal{H}})$. The aim of this paper is to prove that for every finite sequence $(A_{i})_{i=1}^{n}$ of selfadjoint, commuting elements of ${\mathcal{B}}^{+}({\mathcal{H}})$ and every natural number $p\ge 1$, the inequality $\frac{e^{p}}{p^{p}}\Big (\sum _{i=1}^{n}A_{i}^{p}\Big )\le \exp \Big (\sum _{i=1}^{n}A_{i}\Big )\,,$ holds.
References:
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