## Linear Operators, Part 1 |

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Page 131

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. 12

DEFINITION . Let a , u be finitely additive set functions defined on a field E. Then

2 is said to be

0 . v ...

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. 12

DEFINITION . 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 ...

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

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

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