## Linear operators. 2. Spectral theory : self adjoint operators in Hilbert Space |

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Page 893

Let E be a

Let E be a

**bounded**self adjoint spectral measure in Hilbert space defined on a field of subsets of a set S. Then the map Í → T ( f ) defined by the equation T ( f ) = $ ( 8 ) E ( ds ) , fe B ( S , E ) , is a continuous * -homomorphic ...Page 900

and thus there is a

and thus there is a

**bounded**function to on S with f ( s ) = to ( s ) except for s in a set having E measure zero . If f is E - measurable then to is a**bounded**E - measurable function , i.e. , an element of the B * -algebra B ( S , E ) .Page 1240

Semi -

Semi -

**bounded**Symmetric Operators In this section we study the self adjoint extensions of those operators in a class of symmetric operators which arise frequently from the boundary value problems of mathematical physics .### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

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### Other editions - View all

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

### Common terms and phrases

additive adjoint operator algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex 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 matrix measure multiplicity neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero