Joint monotone and boolean numerical and spectral radii of d-tuples of operators

We study joint numerical and spectral radii defined for d-tuples of bounded operators on a Hilbert space and related to noncommutative notions of independence. The definitions are in analogy with the ones of Popescu, where his formulations turned out to be related with free creation operators, and in this way related to the free independence of Voiculescu. In our study the definitions are related with either weakly monotone creation operators, and thus associated with the monotone independence of Muraki, or with boolean creation operators, and hence related with the boolean independence.