## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 24

Page 866

The continuity of the algebraic operations shows that § satisfies the other

requirements for an

also a right, left, or two-sided

3 be a ...

The continuity of the algebraic operations shows that § satisfies the other

requirements for an

**ideal**. Thus the closure of a right, left, or two-sided**ideal**isalso a right, left, or two-sided

**ideal**. This shows that a maximal**ideal**is closed. Let3 be a ...

Page 868

Commutative B-Algebras In case 3 is a commutative B-algebra every

two-sided and the quotient algebra 3/8 is again a commutative algebra. It will be

a B-algebra if Ø is closed (1.13). It is readily seen that every

Commutative B-Algebras In case 3 is a commutative B-algebra every

**ideal**& istwo-sided and the quotient algebra 3/8 is again a commutative algebra. It will be

a B-algebra if Ø is closed (1.13). It is readily seen that every

**ideal**& in 3 which ...Page 1162

Now in an algebra with identity every

an identity is not present this is not true and it becomes an important problem to

find when a closed

Now in an algebra with identity every

**ideal**is contained in a maximal**ideal**, but ifan identity is not present this is not true and it becomes an important problem to

find when a closed

**ideal**is contained in a regular maximal**ideal**. Theorem 4.8 ...### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

48 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 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