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If $f$ takes values in $L(H,L(H,\Bbb R))$ and $μ$ is a $H\hat ⊗_πH$-valued measure, how are $\int f\:dμ$ and $\int f⊗_π\text{id}_Hdμ$ related?
Let
$H$ be a separable $\mathbb R$-Hilbert space
$H\:\hat\otimes_\pi\:H$ denote the projective tensor product of $H$ and $H$
$(\Omega,\mathcal A)$ be a measurable space
$\mu$ be a $H\:\hat\otimes_\pi\...
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Bochner integrals with values in a Hilbert $A$-module
I'm wondering whether there exists a generalisation of Bochner integration with values in a Hilbert $A$-module $M$, where $A$ is a general $C^*$-algebra rather than $\mathbb{C}$ (and whether there are ...
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