Annals of Functional Analysis

A bounded transform approach to self-adjoint operators: Functional calculus and affiliated von Neumann algebras

Christian Budde and Klaas Landsman

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Spectral theory and functional calculus for unbounded self-adjoint operators on a Hilbert space are usually treated through von Neumann’s Cayley transform. Using ideas of Woronowicz, we redevelop this theory from the point of view of multiplier algebras and the so-called bounded transform (which establishes a bijective correspondence between closed operators and pure contractions). This also leads to a simple account of the affiliation relation between von Neumann algebras and self-adjoint operators.

Article information

Ann. Funct. Anal., Volume 7, Number 3 (2016), 411-420.

Received: 20 July 2015
Accepted: 10 December 2015
First available in Project Euclid: 17 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47B25: Symmetric and selfadjoint operators (unbounded)
Secondary: 46L10: General theory of von Neumann algebras

bounded transform self-adjoint operators von Neumann algebras


Budde, Christian; Landsman, Klaas. A bounded transform approach to self-adjoint operators: Functional calculus and affiliated von Neumann algebras. Ann. Funct. Anal. 7 (2016), no. 3, 411--420. doi:10.1215/20088752-3605384.

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