## 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

The Hermitian operators are a subclass of B(S)) which play a role in B(S) much

resembling the role of the real numbers as a subclass of the class of all

...

The Hermitian operators are a subclass of B(S)) which play a role in B(S) much

resembling the role of the real numbers as a subclass of the class of all

**complex****numbers**. In particular, every Te B(S)) can be written uniquely in the form T = A + i...

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

34 other sections not shown

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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