## Linear Operators: Spectral theory |

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Page 1180

(66) sup y”(r) = |x|, a e B; w" e Yand that in consequence Corollary 22 is valid for

functions f(r, s) with values in

with hardly any change in its proof, to the space of functions f with values in any ...

(66) sup y”(r) = |x|, a e B; w" e Yand that in consequence Corollary 22 is valid for

functions f(r, s) with values in

**Hilbert space**. Therefore, Corollary 23 generalizes,with hardly any change in its proof, to the space of functions f with values in any ...

Page 1262

28 Let a self adjoint operator A in a

there exists a

that Aa' = PQa', a e \), P denoting the orthogonal projection of S), on S). 29 Let {T,}

...

28 Let a self adjoint operator A in a

**Hilbert space**X5 with 0 < A = I be given. Thenthere exists a

**Hilbert space**or DS), and an orthogonal projection Q in S), suchthat Aa' = PQa', a e \), P denoting the orthogonal projection of S), on S). 29 Let {T,}

...

Page 1773

APPENDIX

numbers, together with a complex function (-, -) defined on S) × S3 with the

following properties: (i) (a, a.) = 0 if and only if a = 0; (ii) (a, ar) > 0, a e S); (iii) (a +

y, ...

APPENDIX

**Hilbert space**is a linear vector space $) over the field 4 of complexnumbers, together with a complex function (-, -) defined on S) × S3 with the

following properties: (i) (a, a.) = 0 if and only if a = 0; (ii) (a, ar) > 0, a e S); (iii) (a +

y, ...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

48 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

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additive adjoint adjoint operator algebra analytic assume B-algebra basis belongs Borel set boundary conditions boundary values bounded called clear closed closure coefficients commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension fact finite follows formal differential operator formula function function f given Hence Hilbert space ideal identity independent indices inequality integral interval isometric isomorphism Lemma linear mapping matrix measure multiplicity neighborhood norm normal operator obtained positive preceding present projection proof properties prove range regular representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique unit vanishes vector zero