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

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Page 1218

Let

Let

**u**be a finite positive regular measure on the Borel sets of a topological space R. Then , for every B - space valued**u**-**measurable**function f on R and ...Page 1220

If this statement is false , there is a bounded Borel set e with

If this statement is false , there is a bounded Borel set e with

**u**( e ) = | E ... 2 ) , ... , W. ( :, 2 ) are linearly dependent is**u**-**measurable**( cf.Page 1341

If { mij } is the matrix of densities of Hij with respect to ul , then there exist nonnegative

If { mij } is the matrix of densities of Hij with respect to ul , then there exist nonnegative

**u**-**measurable**functions Vi , i = 1 , ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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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 |

### 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