Borel functional calculus
BRANCH OF FUNCTIONAL ANALYSIS
Measurable functional calculus; Resolution of the identity; Completeness relation; Continuous basis; Completeness condition
In functional analysis, a branch of mathematics, the Borel functional calculus is a functional calculus (that is, an assignment of operators from commutative algebras to functions defined on their spectra), which has particularly broad scope. Thus for instance if T is an operator, applying the squaring function s → s2 to T yields the operator T2.