## Linear Operators: Spectral theory |

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Page 950

the

compact group, its existence and uniqueness was proved in Theorem 1.1. The

reader who is unfamiliar with

under the ...

the

**Haar measure**may be taken to be Lebesgue measure: in the case of acompact group, its existence and uniqueness was proved in Theorem 1.1. The

reader who is unfamiliar with

**Haar measure**may wish to consult the remarksunder the ...

Page 1152

The existence of an invariant

countability was first shown by

discussed by von Neumann [17]. Other proofs of existence or uniqueness have ...

The existence of an invariant

**measure**on a group satisfying the second axiom ofcountability was first shown by

**Haar**[1], and the question of uniqueness was firstdiscussed by von Neumann [17]. Other proofs of existence or uniqueness have ...

Page 1154

o-compact group R and let à be a

2 × 2 is a

locally compact and g-compact, it has a

o-compact group R and let à be a

**Haar measure**in R. Then the product measure2 × 2 is a

**Haar measure**in RX R. PRoof. Since the product group Roo – R × R islocally compact and g-compact, it has a

**Haar measure**A*) defined on its Borel ...### What people are saying - Write a review

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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