## Linear Operators: Spectral theory |

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The preceding paragraph indicates that it is of interest to inquire when a given operator A in a

The preceding paragraph indicates that it is of interest to inquire when a given operator A in a

**Hilbert space**can be extended ( in some sense ) to an operator B in a**Hilbert space**, containing ý , in such a way that B has properties ...Page 1180

( 66 ) sup \ y * ( x ) ) = \ al , X E B ; y * EY * and that in consequence Corollary 22 is valid for functions f ( x , s ) with values in

( 66 ) sup \ y * ( x ) ) = \ al , X E B ; y * EY * and that in consequence Corollary 22 is valid for functions f ( x , s ) with values in

**Hilbert space**. Therefore , Corollary 23 generalizes , with hardly any change in its proof ...Page 1262

28 Let a self adjoint operator A in a

28 Let a self adjoint operator A in a

**Hilbert space**H with O SA SI be given . Then there exists a**Hilbert space**H , 2H , and an orthogonal projection Q in H , such that Ax PQx , 2 e 5 , P denoting the orthogonal projection of Hi on H.### 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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additive Akad 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