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

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Page 879

It is clear that the smallest closed subalgebra of B ( H ) which

It is clear that the smallest closed subalgebra of B ( H ) which

**contains**a normal operator T , its adjoint T * , and the identity I is a commutative B ...Page 995

If y and f are in L. ( R ) and L ( R ) respectively and if f ( m ) O for every m in the spectral set o ( Q ) , then off * 9 )

If y and f are in L. ( R ) and L ( R ) respectively and if f ( m ) O for every m in the spectral set o ( Q ) , then off * 9 )

**contains**no isolated points .Page 996

From Lemma 12 ( b ) it is seen that olf * 9 ) Cole ) and from Lemma 12 ( c ) and the equation of = Tf it follows that o ( f * Q )

From Lemma 12 ( b ) it is seen that olf * 9 ) Cole ) and from Lemma 12 ( c ) and the equation of = Tf it follows that o ( f * Q )

**contains**no interior point ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

37 other sections not shown

### 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