## Linear Operators: General theory |

### From inside the book

Results 1-3 of 78

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 & # 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

is odd , the

n is even , the

...

79 The

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

**inequality**fa ' ( 0 ) < n max ( x ( t ) - 1515 + 1 holds for each x in Pn . Ifn is even , the

**inequality**lx ' ( 0 ) = ( n - 1 ) max | æ ( t ) - 1 Sis + 1 holds for each x...

### What people are saying - Write a review

User Review - Flag as inappropriate

i want to read

### Contents

Special Spaces | 237 |

Convex Sets and Weak Topologies | 409 |

General Spectral Theory | 555 |

Copyright | |

5 other sections not shown

### Other editions - View all

### Common terms and phrases

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