## Linear Operators: Spectral theory |

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Page 1061

14 ) and Hölder ' s

E . D . Having proved the basic

the full

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 , we now proceed to provethe full

**inequality**of Calderón and Zygmund . Our first step is to put the result of ...Page 1105

We now pause to sharpen another of the

continuity of the product TS which was noted in the paragraph following Lemma 9

, the continuity of the norm function which follows from the triangle

Lemma ...

We now pause to sharpen another of the

**inequalities**of Lemma 9 . ... thecontinuity of the product TS which was noted in the paragraph following Lemma 9

, the continuity of the norm function which follows from the triangle

**inequality**ofLemma ...

Page 1774

The above

follows from the postulates for H that the Schwarz

is zero . Hence suppose that x # 0 # y . For an arbitrary complex number a 0 = ( x

...

The above

**inequality**, known as the Schwarz**inequality**, will be proved first . Itfollows from the postulates for H that the Schwarz

**inequality**is valid if either x or yis zero . Hence suppose that x # 0 # y . For an arbitrary complex number a 0 = ( x

...

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### Contents

BAlgebras | 861 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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