Spectral measure

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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)
How to Cite This Entry:
Spectral measure. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by V.S. Shul'man (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article