Dilation Theory Yesterday and Today
Paul Halmos’ work in dilation theory began with a question and its answer: Which operators on a Hilbert space H can be extended to normal operators on a larger Hilbert space K ⊇ H? The answer is interesting and subtle.
The idea of representing operator-theoretic structures in terms of conceptually simpler structures acting on larger Hilbert spaces has become a central one in the development of operator theory and, more generally, non-commutative analysis. The work continues today. This article summarizes some of these diverse results and their history.
Mathematics Subject Classification (2000)46L07
KeywordsDilation theory completely positive linear maps
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