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Graduate Seminar Series

Mon., Nov. 28, 2022 3:30 p.m.

Location: Live Stream

Speaker: Patrick Melanson

Title: Completely Bounded Maps, Stinespring Representation, and Uniqueness (506 kB) PDF file


In operator theory, an object of great relevance is the completely positive map. Much has already been explored on the topic, though the conditions on these mappings is rather restrictive. We ask, then, if there is a more general notion. To this end, we introduce completely bounded maps. From here, we will look at which properties translate nicely to this more general context, and which ones are problematic. Specifically, we will focus on the Stinespring representation for completely bounded maps, and ask under what conditions is this representation unique.

Live Stream: