## Linear Operators, Part 1 |

### From inside the book

Results 1-3 of 73

Page 224

Functions of a Complex Variable In some of the chapters to follow , and

especially in Chapter VII , we shall use extensions of certain well - known results

in the theory of

functions ...

Functions of a Complex Variable In some of the chapters to follow , and

especially in Chapter VII , we shall use extensions of certain well - known results

in the theory of

**analytic**functions of a complex variable to the case where thefunctions ...

Page 586

Then there exists a 8 > 0 such that if u < d , then Ū CO ( T ( u ) ) and R ( 2 ; T ( u ) )

is an

such that if sul < $ , then U CO ( T ( u ) ) . Let S < d be chosen such that T ( 0 ) - T ...

Then there exists a 8 > 0 such that if u < d , then Ū CO ( T ( u ) ) and R ( 2 ; T ( u ) )

is an

**analytic**function of u for each a € U . PROOF . By Lemma 3 , there is a & ,such that if sul < $ , then U CO ( T ( u ) ) . Let S < d be chosen such that T ( 0 ) - T ...

Page 588

Consequently , it is possible to solve for the tij , and obtain in each case the

quotient of an

0 , its reciprocal , and therefore each tij , is

...

Consequently , it is possible to solve for the tij , and obtain in each case the

quotient of an

**analytic**function by 4 ( u ) . Since , for su < 09 , the function A ( u ) =0 , its reciprocal , and therefore each tij , is

**analytic**. Thus the tij are**analytic**for lul...

### 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 |

Algebraic Preliminaries | 34 |

Copyright | |

12 other sections not shown

### Other editions - View all

### Common terms and phrases

Akad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex condition Consequently contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint element 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 meaning measure space metric neighborhood norm obtained operator positive measure problem Proc PROOF properties proved regular respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement subset sufficient Suppose Theorem theory topology transformations u-measurable uniform uniformly unique unit valued vector weak weakly compact zero