## Linear Operators: Spectral theory |

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Page 1191

However, this

that any function g with a continuous first derivative has the property that (#1 -(, ; *

(i. 'd *)- hijo, fe i}). and thus any such g, even though it fails to vanish at one of the

...

However, this

**operator**is not self**adjoint**for it is clear from the above equationsthat any function g with a continuous first derivative has the property that (#1 -(, ; *

(i. 'd *)- hijo, fe i}). and thus any such g, even though it fails to vanish at one of the

...

Page 1270

The problem of determining whether a given symmetric

theorem may be employed. If the answer to this problem is affirmative, it is

important to ...

The problem of determining whether a given symmetric

**operator**has a self**adjoint**extension is of crucial importance in determining whether the spectraltheorem may be employed. If the answer to this problem is affirmative, it is

important to ...

Page 1548

extensions of S and S respectively, and let A,(T) and 2,07) be the numbers

defined for the self adjoint operators T and T as in Exercise D2. Show that A, T) >

A,(T), n > 1. D11 Let T. be a self

be a ...

extensions of S and S respectively, and let A,(T) and 2,07) be the numbers

defined for the self adjoint operators T and T as in Exercise D2. Show that A, T) >

A,(T), n > 1. D11 Let T. be a self

**adjoint operator**in Hilbert space $31, and let Tobe a ...

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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 |

### Common terms and phrases

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