Dilation Theory Yesterday and Today

  • William Arveson
Part of the Operator Theory Advances and Applications book series (OT, volume 207)


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 KH? 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)



Dilation theory completely positive linear maps 


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© Springer Basel AG 2010

Authors and Affiliations

  • William Arveson
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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