Just a translation issue. I'm italian and my professor of spectral theory wrote the list to the arguments to be studied in italian. The problem is that all the literature is in english and often the translation are a bit fanciful and I can't find the respective arguments in the books! In particular I can't find the analogous of "operatori di allacciamento", which can be translated in english like "Hook up operators" or "Enlace operator" or maybe "Connection operators". In the list they are near the states and representation of a C*Algebra and Subrepresentation. Any idea of what these "hook up operators" may they be?

It seems that you are looking for interwining operators.