## Linear operators. 2. Spectral theory : self adjoint operators in Hilbert Space |

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Page 860

A B -

A B -

**algebra**X is commutative in case xy yx for all x and y in X. An involution in a B -**algebra**X is a mapping x → ** of X into itself with the properties ( x + y ) * = x * + y * , ( xy ) * = y * r * ( ax ) * ār * , ( x * ) * = X ...Page 868

Commutative B - Algebras In case X is a commutative B -

Commutative B - Algebras In case X is a commutative B -

**algebra**every ideal I is two - sided and the quotient**algebra**X / F is again a commutative**algebra**. It will be a B -**algebra**if I is closed ( 1.13 ) .Page 979

One of these algebras , namely the

One of these algebras , namely the

**algebra**U of the preceding section , we have met before . For convenience , its definition and some of its properties will be restated here . For every f in L ( R ) the convolution ( * * g ) ( x ) ...### 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 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

### Common terms and phrases

additive adjoint operator algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex 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 matrix measure multiplicity neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero