## Linear Operators: Spectral theory |

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Page 868

If S is a closed ideal in the commutative B-algebra 3. then the quotient algebra 3/

8 is isometrically isomorphic to the field of

marimal. PRoof. If & is not maximal it is properly contained in an ideal and so 3/3

...

If S is a closed ideal in the commutative B-algebra 3. then the quotient algebra 3/

8 is isometrically isomorphic to the field of

**complex numbers**if and only if 3 ismarimal. PRoof. If & is not maximal it is properly contained in an ideal and so 3/3

...

Page 872

The number a (A) is clearly independent of the particular sequence {P,} used to

define it. For a fixed Ao e G the map w -> a.(Wo) is a homomorphism of 3 into the

field of

The number a (A) is clearly independent of the particular sequence {P,} used to

define it. For a fixed Ao e G the map w -> a.(Wo) is a homomorphism of 3 into the

field of

**complex numbers**. Thus by Lemma 2 there is a maximal ideal ost, with a ...Page 906

Unitary operators have a number of other characteristic properties. For example,

if U is unitary then (a, ... at the end of the chapter. The relation between unitary

operators and

Unitary operators have a number of other characteristic properties. For example,

if U is unitary then (a, ... at the end of the chapter. The relation between unitary

operators and

**complex numbers**of unit modulus, Hermitian operators and ...### What people are saying - Write a review

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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### Common terms and phrases

additive Akad algebra Amer analytic applied assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complete Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function function f given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math measure multiplicity neighborhood norm obtained partial positive preceding present problem projection PRoof properties prove range regular remark representation respectively restriction result satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero