## Linear Operators: General theory |

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Page 289

that there is a functional y * € L * such that 2 * * ( * * ) = y * ( g ) when g and x * are

connected , as in Theorem 1 , by the formula * * 1 = 15 / ( 8 ) g ( s ) u ( ds ) , f € Lp

...

**Proof**. Let x * * € ( L ) * . By Theorem 1 , L * is isometrically isomorphic to Lq , sothat there is a functional y * € L * such that 2 * * ( * * ) = y * ( g ) when g and x * are

connected , as in Theorem 1 , by the formula * * 1 = 15 / ( 8 ) g ( s ) u ( ds ) , f € Lp

...

Page 415

Hence ko e p - A , and thus pe A + ko CA + K . Q . E . D . - Since the commutativity

of the group G is not essential to the

Abelian topological groups . 4 LEMMA . For arbitrary sets A , B in a linear space X

: ( i ) ...

Hence ko e p - A , and thus pe A + ko CA + K . Q . E . D . - Since the commutativity

of the group G is not essential to the

**proof**, the same result holds for non -Abelian topological groups . 4 LEMMA . For arbitrary sets A , B in a linear space X

: ( i ) ...

Page 699

The

11 as outlined in the diagram : C = CPx + DPx = Dx = Cx . The

implication CPx = DPx which is the

of ...

The

**proof**of this lemma is the most involved of all the steps in the**proof**of Lemma11 as outlined in the diagram : C = CPx + DPx = Dx = Cx . The

**proof**of theimplication CPx = DPx which is the

**proof**of Lemma 14 is very similar to the**proof**of ...

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### Contents

Metric Spaces | 19 |

Convergence and Uniform Convergence of Generalized | 26 |

Exercises | 33 |

Copyright | |

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