## Linear Operators: Spectral theory |

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Page 866

Thus the closure of a right , left , or two - sided

sided

Thus the closure of a right , left , or two - sided

**ideal**is also a right , left , or two -sided

**ideal**. ... Let I be a right**ideal**and order by inclusion the family of all right**ideals**which contain J . An application of Zorn ' s lemma shows that this family ...Page 868

Commutative B - Algebras In case X is a commutative B - algebra every

two - sided and the quotient algebra X / I is again a commutative algebra . It will

be a B - algebra if I is closed ( 1 . 13 ) . It is readily seen that every

Commutative B - Algebras In case X is a commutative B - algebra every

**ideal**I istwo - sided and the quotient algebra X / I is again a commutative algebra . It will

be a B - algebra if I is closed ( 1 . 13 ) . It is readily seen that every

**ideal**I in X ...Page 1162

is isomorphic with the complex field , and it turns out that the regular maximal

with identity every

is isomorphic with the complex field , and it turns out that the regular maximal

**ideals**of L ( R ) are in one - to - one ... the point at infinity of M . Now in an algebrawith identity every

**ideal**is contained in a maximal**ideal**, but if an identity is not ...### What people are saying - Write a review

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### Contents

IX | 859 |

extensive presentation of applications of the spectral theorem | 911 |

Miscellaneous Applications | 937 |

Copyright | |

20 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

additive adjoint adjoint operator algebra analytic assume B-algebra basis belongs Borel set boundary conditions boundary values bounded called clear closed closure coefficients commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension fact finite follows formal differential operator formula function function f give given Hence Hilbert space ideal identity independent indices inequality integral interval isometric isomorphism Lemma linear mapping matrix measure multiplicity neighborhood norm normal operator obtained positive preceding present projection proof properties prove range regular representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique unit vanishes vector zero