## Linear Operators, Part 1 |

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Page 239

It consists of ordered n - tuples x = 0 , ... , .n ] On and has the

x = { } p . 3 . The space 1 " is the linear space of all ordered n - tuples 21 , ... , an ]

of scalars Oy , . ... , den with the

It consists of ordered n - tuples x = 0 , ... , .n ] On and has the

**norm**of scalars 0.13x = { } p . 3 . The space 1 " is the linear space of all ordered n - tuples 21 , ... , an ]

of scalars Oy , . ... , den with the

**norm**\ w \ = sup loilo 1Sisn 4. The space 1 , is ...Page 240

The space bs is the linear space of all sequences x = { n } of scalars for which the

sequences x = { an } for which the series Anal On is convergent . The

sup ...

The space bs is the linear space of all sequences x = { n } of scalars for which the

**norm**n sup ail n i = 1 is finite . 11. The space cs is the linear space of allsequences x = { an } for which the series Anal On is convergent . The

**norm**is n =sup ...

Page 472

168 ] showed that the

and only if the function x , achieves its maximum at exactly one point . Mazur ( 1 ;

p . 78–79 ) proved that the same condition holds in B ( S ) , that the

168 ] showed that the

**norm**in C [ 0 , 1 ] is strongly differentiable at x , e C [ 0 , 1 ] ifand only if the function x , achieves its maximum at exactly one point . Mazur ( 1 ;

p . 78–79 ) proved that the same condition holds in B ( S ) , that the

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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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