Abstract
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.
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Arveson, W. (2010). Dilation Theory Yesterday and Today. In: Axler, S., Rosenthal, P., Sarason, D. (eds) A Glimpse at Hilbert Space Operators. Operator Theory Advances and Applications, vol 207. Springer, Basel. https://doi.org/10.1007/978-3-0346-0347-8_8
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