## Linear Operators: General theory |

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Page 54

A linear mapping of one F - space into another is continuous if and only if it maps

linear and continuous , and let B C X be

A linear mapping of one F - space into another is continuous if and only if it maps

**bounded**sets into**bounded**sets . Proof . Let X , Y be F - spaces , let T : x + y belinear and continuous , and let B C X be

**bounded**. For every neighborhood V of ...Page 97

and to be

function u is important because it dominates u in the sense that v ( u , E ) 2 \ u ( E

) for E € { ; the reader should test his comprehension of Definition 4 below by ...

and to be

**bounded**if u is**bounded**. The total variation v ( u ) of an additive setfunction u is important because it dominates u in the sense that v ( u , E ) 2 \ u ( E

) for E € { ; the reader should test his comprehension of Definition 4 below by ...

Page 345

if and only if it is

and each j = 0 , 1 , . . . , p . ( c ) Co is not weakly complete , and not reflexive . ( d )

A subset A Ç CP is conditionally compact if and only if it is

if and only if it is

**bounded**and f ( s ) converges ( to f ( ' \ ( s ) ) for each s in [ a , b ]and each j = 0 , 1 , . . . , p . ( c ) Co is not weakly complete , and not reflexive . ( d )

A subset A Ç CP is conditionally compact if and only if it is

**bounded**and for ...### What people are saying - Write a review

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### Contents

Special Spaces | 237 |

Convex Sets and Weak Topologies | 409 |

General Spectral Theory | 555 |

Copyright | |

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