Dilation theory yesterday and today

Details Dilation theory yesterday and today Dilation theory yesterday and today

2009-02-23

arxiv.org/abs/0902.3989v2

Mathematics

Operator Algebras

24 pages, contributed to a volume commemorating the work of Paul Halmos

Scientific paper

Paul Halmos' work in dilation theory began with a question and its answer: Which operators on a Hilbert space can be extended to normal operators on a larger Hilbert space? 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, noncommutative analysis. The work continues today. In this article we summarize some of these diverse results and their history.

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