## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 90

Page 1379

{6,6} is the matrix measure of

determined for each e C N. Since A is the union of a sequence of neighborhoods

of the same type as N, the uniqueness of {6,3 follows immediately. Q.E.D. 27

{6,6} is the matrix measure of

**Theorem**23, the values 6,(e) are uniquelydetermined for each e C N. Since A is the union of a sequence of neighborhoods

of the same type as N, the uniqueness of {6,3 follows immediately. Q.E.D. 27

**THEOREM**.Page 1591

The defining property used by them coincides with the property we have given in

extensive use of Definition 1, has also been used by $nol [1] and Naimark [5].

The defining property used by them coincides with the property we have given in

**Theorem**4. The development followed in this section and the next, which makesextensive use of Definition 1, has also been used by $nol [1] and Naimark [5].

Page 1904

(See also Ergodic

5.32 (584) by inverting sequences, VIII.2.13 (650) study of, VII.7. for kernels, III.

12.10–12 (219–222) Lebesgue dominated convergence

(See also Ergodic

**theorems**) in general spaces, VII.3.13 (571), VII.3.23 (576), VII.5.32 (584) by inverting sequences, VIII.2.13 (650) study of, VII.7. for kernels, III.

12.10–12 (219–222) Lebesgue dominated convergence

**theorem**, III.3.7 (124), III.### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

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### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

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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