Abstract
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.
Citation
Christian Budde. Klaas Landsman. "A bounded transform approach to self-adjoint operators: Functional calculus and affiliated von Neumann algebras." Ann. Funct. Anal. 7 (3) 411 - 420, August 2016. https://doi.org/10.1215/20088752-3605384
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