## Linear Operators, Part 2 |

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Page 1061

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

Thus sup stof ( x ) g ( x ) dx = Kello's p ' 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 5 that the Schwarz**inequality**is valid if either x or y is zero . Hence suppose that & # 0 #y . For an arbitrary complex ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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