## Linear Operators: General theory |

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Page 121

We observe that the

functions ) the

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

is ...

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

**inequality**. To see that itis ...

Page 248

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

...

Page 370

Nelson Dunford, Jacob T. Schwartz, William G. Bade. and the equality is attained

only by scalar multiples of the Tchebicheff polynomial τη . 79 The

( 1 ) | Sno max ( 1 ) - 1 Sts1 holds for each x in Pn . 80 If n is odd , the

Nelson Dunford, Jacob T. Schwartz, William G. Bade. and the equality is attained

only by scalar multiples of the Tchebicheff polynomial τη . 79 The

**inequality**| | go( 1 ) | Sno max ( 1 ) - 1 Sts1 holds for each x in Pn . 80 If n is odd , the

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### Contents

B Topological Preliminaries | 10 |

quences | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

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