A unitary homomorphism from some Boolean algebra of sets into the Boolean algebra of projection operators on a Banach space. Every operator on a Banach space defines a spectral measure on the set of open-and-closed subsets of its spectrum by the formula
where is a Jordan curve separating from . Here, and . The construction of spectral measures satisfying these conditions on wider classes of Boolean algebras of sets is one of the basic problems in the spectral theory of linear operators.
|[1a]||N. Dunford, J.T. Schwartz, "Linear operators. Spectral operators" , 3 , Interscience (1971)|
|[1b]||N. Dunford, J.T. Schwartz, "Linear operators. Spectral theory" , 2 , Interscience (1963)|
Spectral measure. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Spectral_measure&oldid=17065