## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 88

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

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