## 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

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 1048

Each point a in E. may be written uniquely as a = ro, where re R, a e S, and the

mapping [r, o] → a = roo is evidently a homeomorphism of R xS onto E. Thus the

o-

Each point a in E. may be written uniquely as a = ro, where re R, a e S, and the

mapping [r, o] → a = roo is evidently a homeomorphism of R xS onto E. Thus the

o-

**field**3, of Borel subsets of E. is the product o-**field**of the g-**field**&n of Borel ...Page 1153

Thus the product group has a Haar measure A*) defined on its Borel

is natural to expect that the product measure AxA coincides, up to a constant

multiple, with 29. This fact will be established in Theorem 7. 6 LEMMA. Let the

locally ...

Thus the product group has a Haar measure A*) defined on its Borel

**field**20°). Itis natural to expect that the product measure AxA coincides, up to a constant

multiple, with 29. This fact will be established in Theorem 7. 6 LEMMA. Let the

locally ...

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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