## Linear Operators: Spectral theory |

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Page 1272

If T is a symmetric operator with dense domain, then it has proper symmetric

extensions provided both of its deficiency

marimal symmetric operator is one which has no proper symmetric extensions;

hence, ...

If T is a symmetric operator with dense domain, then it has proper symmetric

extensions provided both of its deficiency

**indices**are different from zero. Amarimal symmetric operator is one which has no proper symmetric extensions;

hence, ...

Page 1398

Let r be a formally self adjoint formal differential operator defined on an interval I.

If the minimum of the deficiency

equation to - Aa has at least k linearly independent solutions in L2(I). Proof. By

Theorem ...

Let r be a formally self adjoint formal differential operator defined on an interval I.

If the minimum of the deficiency

**indices**of To(r) is k, then for A £ o.(1) theequation to - Aa has at least k linearly independent solutions in L2(I). Proof. By

Theorem ...

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

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 ...### What people are saying - Write a review

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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