## Linear Operators: General theory |

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Page 120

Sst ( s ) g ( s ) u ( ds ) < Wolle . Proof . The function y ( t ) = { " / p + t- / q has a

positive derivative for t > 1 , and a negative derivative for 0 < t < 1. Hence , its

minimum value for t > 0 is q ( 1 ) = 1. If we put t = alla b - 1 / P we obtain the

Sst ( s ) g ( s ) u ( ds ) < Wolle . Proof . The function y ( t ) = { " / p + t- / q has a

positive derivative for t > 1 , and a negative derivative for 0 < t < 1. Hence , its

minimum value for t > 0 is q ( 1 ) = 1. If we put t = alla b - 1 / P we obtain the

**inequality**ab ...Page 121

... We observe that the

functions ) the

. This observation is obvious in the case of Minkowski's

... We observe that the

**inequality**of Minkowski and ( in the case of scalar valuedfunctions ) the

**inequality**of Hölder may be regarded as applying to the spaces Lp. This observation is obvious in the case of Minkowski's

**inequality**. To see that it ...Page 248

The above

follows from the postulates for H that the Schwarz

is zero . Hence suppose that 8C # 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 8C # 0 #y . For an arbitrary complex number a 0 = (

x ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

80 other sections not shown

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