## Linear Operators: General theory |

### From inside the book

Results 1-3 of 79

Page 121

... observe that the

functions ) the

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

is ...

... 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 # # 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 # # 0 # y . For an arbitrary complex number a 0 = ( x

...

Page 370

79 The

n is odd , the

. If n is even , the

79 The

**inequality**\ x ' ( 1 ) | S na max | æ ( t ) | - 1 Sisi holds for each x in Pn . 80 Ifn is odd , the

**inequality**la ' ( 0 ) Sn max ( x ( t ) | | - 1 Sis + 1 holds for each x in Pn. If n is even , the

**inequality**Ta ' ( 0 ) = ( n - 1 ) max \ æ ( t ) | | - 1515 + 1 holds ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

21 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex Consequently constant contains converges convex Corollary defined DEFINITION denote dense determined differential disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows formula function defined function f given Hence Hilbert space identity implies inequality integral interval Lebesgue Lemma limit linear functional linear operator linear space Math mean measure space metric neighborhood norm positive measure problem Proc projection PROOF properties proved respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement strongly subset sufficient Suppose Theorem theory topological space topology transformations u-measurable uniform uniformly unique unit valued vector weak weakly compact zero