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

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Page 955

For the remainder of this section A will

For the remainder of this section A will

**denote**the B * -algebra of operators A , { al } , where I is the identity operator in the Hilbert space L ( R ) , and where X , is the closure of A , in the uniform operator topology .Page 1126

of the closed set C ; we shall

of the closed set C ; we shall

**denote**this subspace of L [ 0 , 1 ] by the symbol † ( C ) . Since each projection in the spectral resolution of T and hence each continuous function of T is a strong limit of linear combinations of the ...Page 1673

Let C

Let C

**denote**the parallelepiped C = { x € E " \ a ; S x ; < bj , isis n } , For each 1 > 0 such that ^ < bı - ay , let M ,**denote**the mapping of C into itself defined by the equations M [ X13 M [ X1 , ...### 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