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arXiv · 1508.06772

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

Christian Budde·Klaas Landsman
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Abstract

Spectral theory and functional calculus for unbounded self-adjoint operators on a Hilbert space are usually treated through von Neumann's Cayley transform. Based on 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.

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Christian Budde, Klaas Landsman. 2015-08-27. A bounded transform approach to self-adjoint operators: Functional calculus and affiliated von Neumann algebras. https://doi.org/10.1215/20088752-3605384

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