# Semispectral Measures and Feller markov Kernels

@article{Beneduci2012SemispectralMA, title={Semispectral Measures and Feller markov Kernels}, author={Roberto Beneduci}, journal={arXiv: Functional Analysis}, year={2012} }

We give a characterization of commutative semispectral measures by means of Feller and Strong Feller Markov kernels. In particular:
{itemize} we show that a semispectral measure $F$ is commutative if and only if there exist a self-adjoint operator $A$ and a Markov kernel $\mu_{(\cdot)}(\cdot):\Gamma\times\mathcal{B}(\mathbb{R})\to[0,1]$, $\Gamma\subset\sigma(A)$, $E(\Gamma)=\mathbf{1}$, such that $$F(\Delta)=\int_{\Gamma}\mu_{\Delta}(\lambda)\,dE_{\lambda},$$ \noindent and $\mu_{(\Delta)}$ is…

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