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The mathematical legacy of William Arveson. (English) Zbl 1260.47001
This paper is a short retrospective of William Arveson’s contributions to the operator theory and operator algebras. More specifically, his main results on dilation theory, maximal subdiagonal algebras, dynamical systems, invariant subspaces, nest algebras, automorphism groups on \(C^*\) algebras and multivariable operator theory are reviewed.

47-03 History of operator theory
01A70 Biographies, obituaries, personalia, bibliographies
01A65 Development of contemporary mathematics
47A20 Dilations, extensions, compressions of linear operators
47A15 Invariant subspaces of linear operators
47D03 Groups and semigroups of linear operators
47L30 Abstract operator algebras on Hilbert spaces
47L35 Nest algebras, CSL algebras
46L40 Automorphisms of selfadjoint operator algebras
46L55 Noncommutative dynamical systems
47A13 Several-variable operator theory (spectral, Fredholm, etc.)
Biographic References:
Arveson, William Barnes
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