## Linear Operators, Part 1 |

### From inside the book

Results 1-3 of 87

Page 131

Let a , u be finitely additive set functions defined on a field E. Then 2 is said to be

> 0 The function 2 is said to be u - singular if there is a set E , e { such that v ( u ...

Let a , u be finitely additive set functions defined on a field E. Then 2 is said to be

**continuous**with respect to u or simply l -**continuous**, if lim 2 ( E ) = 0 . v ( u , E ) -> 0 The function 2 is said to be u - singular if there is a set E , e { such that v ( u ...

Page 454

If { k } is another such minimizing sequence converging to q ' € K , then IV.4.2

implies that { kį , kí , ką , ka , ... } is also convergent . Hence q = q ' and q is the

desired nearest point N ( p ) . Now , N ( p ) is a

pm → p ...

If { k } is another such minimizing sequence converging to q ' € K , then IV.4.2

implies that { kį , kí , ką , ka , ... } is also convergent . Hence q = q ' and q is the

desired nearest point N ( p ) . Now , N ( p ) is a

**continuous**function of p . For , ifpm → p ...

Page 513

12 If H is a Hilbert space , the mapping T → T * of B ( v ) into itself is

with either the uniform or weak operator topology . By considering the sequence {

An } defined in Exercise 11 , show that this mapping is not

12 If H is a Hilbert space , the mapping T → T * of B ( v ) into itself is

**continuous**with either the uniform or weak operator topology . By considering the sequence {

An } defined in Exercise 11 , show that this mapping is not

**continuous**in the ...### What people are saying - Write a review

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

### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

87 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 complex Consequently contains converges convex Corollary defined DEFINITION denote dense determined differential dimensional disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space identity implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space Math measure space metric space neighborhood norm open set positive measure problem projection Proof properties proved range reflexive representation respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology u-measurable uniform uniformly unique unit valued vector weak weakly compact zero