# Spectral measure

From Encyclopedia of Mathematics

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.

#### References

[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: http://encyclopediaofmath.org/index.php?title=Spectral_measure&oldid=17065

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