## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 82

Page 1902

Closed orthonormal system,

sphere, II.3.1 (59) Closure of a set, criterion to be in, I.7.2 (27)

...

Closed orthonormal system,

**definition**, IV.14.1 (357) study of, IV.14 Closed set,**definition**, I.4.3 (10) properties, I.4.4–5 (10) Closed sphere, II.4.1 (70) Closed unitsphere, II.3.1 (59) Closure of a set, criterion to be in, I.7.2 (27)

**definition**, I.4.9 (11)...

Page 1907

Essentially bounded,

separably valued,

of a function, by continuity, I.6.17 (23)

17) ...

Essentially bounded,

**definition**, III.1.11 (100–101) E-, X.2 (899) Essentiallyseparably valued,

**definition**, III.1.11 ...**definitions**, (3) topology of, (11) Extensionof a function, by continuity, I.6.17 (23)

**definition**, (3) Tietze's theorem, I.5.3–4 (15–17) ...

Page 1921

T Tangent function,

properties, V.9.1 (445), V.9.3 (446), ... base and subbase for, I.4.6 (10) basic

3.2 (419) ...

T Tangent function,

**definition**, V.9.2 (446) examples, V.11.9–13 (458–459)properties, V.9.1 (445), V.9.3 (446), ... base and subbase for, I.4.6 (10) basic

**definitions**, I.4.1 (10) bounded 3' topology, V.5.3 (427) functional or T topology, V.3.2 (419) ...

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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