Operator Algebras and Unbounded Self-adjoint Operators

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.