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

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Page 1061

Thus ( HT sup SH1 ( ) g ( x ) dx = Kellos by Theorem IV.8.1 , the Hahn - Banach theorem ( II.3.14 ) and Hölder's

Thus ( HT sup SH1 ( ) g ( x ) dx = Kellos by Theorem IV.8.1 , the Hahn - Banach theorem ( II.3.14 ) and Hölder's

**inequality**, and the theorem is proved for all p , 1 < p < 00. Q.E.D. Having proved the basic**inequality**of M. Riesz ...Page 1105

We now pause to sharpen another of the

We now pause to sharpen another of the

**inequalities**of Lemma 9 . ... the continuity of the norm function which follows from the triangle**inequality**of Lemma 14 ( d ) , and by Lemma 11 , it follows that we may without loss of generality ...Page 1774

The above

The above

**inequality**, known as the Schwarz**inequality**, will be proved first . It follows from the postulates for Ý that the Schwarz**inequality**is valid if either x or y is zero . Hence suppose that x 70 #y . For an arbitrary complex ...### What people are saying - Write a review

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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 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