## Linear Operators: Spectral theory |

### From inside the book

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Page 884

The study of ideal theory in B-algebra was inaugurated by Gelfand [1] to whom

most of the results

Section 2 are due to Gelfand [1]. The fundamental Theorem 3.7 was proved by ...

The study of ideal theory in B-algebra was inaugurated by Gelfand [1] to whom

most of the results

**given**in Section 1 are due. B- and B"-algebras. The results ofSection 2 are due to Gelfand [1]. The fundamental Theorem 3.7 was proved by ...

Page 1149

likewise

simple compact groups is

kontinuierlicher halb-einfachen Gruppen durch lineare Transformationen III, Math

.

likewise

**given**by irreducible sets of tensors. The group ... of the five exceptionalsimple compact groups is

**given**in Weyl's memoir Theorie der Darstellungenkontinuierlicher halb-einfachen Gruppen durch lineare Transformationen III, Math

.

Page 1591

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

Theorem 4. The development followed in this section and the next, which makes

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**inTheorem 4. The development followed in this section and the next, which makes

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

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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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 |

### 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