## Linear Operators: Spectral theory |

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Page 1396

Then both deficiency indices of t are

extensions of To(r) have the same set of non-isolated points, and this set is

to o,(r). PRoof. The second assertion follows immediately from Theorem 5 and

Corollary ...

Then both deficiency indices of t are

**equal**. Moreover, all the self adjointextensions of To(r) have the same set of non-isolated points, and this set is

**equal**to o,(r). PRoof. The second assertion follows immediately from Theorem 5 and

Corollary ...

Page 1454

If T is a closed symmetric operator in Hilbert space, and T is bounded below, then

(a) the essential spectrum of T is a subset of the real aris which is bounded below

; (b) the deficiency indices of T are

If T is a closed symmetric operator in Hilbert space, and T is bounded below, then

(a) the essential spectrum of T is a subset of the real aris which is bounded below

; (b) the deficiency indices of T are

**equal**. PRoof. To prove (a), note that if T is ...Page 1735

Let $ in Co(E") be identically

sphere in E" and identically zero outside the sphere of radius 2 in E". We wish to

show that flu is in Hot!)(UI) for some neighborhood U of the origin. We see from ...

Let $ in Co(E") be identically

**equal**to 1 in a neighborhood of the unit closedsphere in E" and identically zero outside the sphere of radius 2 in E". We wish to

show that flu is in Hot!)(UI) for some neighborhood U of the origin. We see from ...

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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