## Linear Operators: General theory |

### From inside the book

Results 1-3 of 67

Page 3

The function f is said to map A onto B if | ( A ) = B and into B if f ( A ) C B. The

function f is said to be an extension of the function g and g a restriction of / if the

The function f is said to map A onto B if | ( A ) = B and into B if f ( A ) C B. The

function f is said to be an extension of the function g and g a restriction of / if the

**domain**off contains the**domain**of g , and f ( x ) = g ( x ) for æ in the**domain**of g .Page 230

Let | be an analytic function defined on a connected

plane and having its values in a complex B - space X. Then | ( z ) does not have

its maximum at any point of the

Let | be an analytic function defined on a connected

**domain**D in the complexplane and having its values in a complex B - space X. Then | ( z ) does not have

its maximum at any point of the

**domain**D , unless \ | ( 2 ) is identically constant .Page 538

Nelson Dunford. G. Some miscellaneous convexity inequalities . 48 ( Hadamard

three circles theorem ) Let f be an analytic function defined in the annular

a < 121 < b and having values in a B - space X. Show that if M ( r ) = max \ | ( z ) ...

Nelson Dunford. G. Some miscellaneous convexity inequalities . 48 ( Hadamard

three circles theorem ) Let f be an analytic function defined in the annular

**domain**a < 121 < b and having values in a B - space X. Show that if M ( r ) = max \ | ( z ) ...

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

80 other sections not shown

### Other editions - View all

### Common terms and phrases

Akad algebra Amer analytic applied arbitrary assume 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 domain element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math mean measure space metric space neighborhood norm o-field open set operator positive problem Proc PROOF properties proved range regular respect Russian satisfies scalar seen 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