## Linear Operators, Part 1 |

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Page 289

there is a functional y” e L. such that w”(v*) = y”(g) when g and r* are connected,

as in Theorem 1, by the formula * = s.sos)(s)usds), fe L, Applying Theorem I once

...

**PRoof**. Let r** e (L.)*. By Theorem 1, L. is isometrically isomorphic to L, so thatthere is a functional y” e L. such that w”(v*) = y”(g) when g and r* are connected,

as in Theorem 1, by the formula * = s.sos)(s)usds), fe L, Applying Theorem I once

...

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and proceed as in the first part of the

a subsequence {y,n} of {a,} such that lim, ... a "y, exists for each w” in the set H of

that

...

and proceed as in the first part of the

**proof**of the preceding theorem to constructa subsequence {y,n} of {a,} such that lim, ... a "y, exists for each w” in the set H of

that

**proof**. Let K, - cosy, y, 1,...} and let yo be an arbitrary point in O ._i K. For each...

Page 699

dy Vot Jo 2y” 2e-vo - - A - eTV t, Vot which proves (*) and completes the

the lemma. Q.E.D. We shall now state and prove the lemma referred to as CP. For

technical reasons occurring later the following lemma is stated for what might be

...

dy Vot Jo 2y” 2e-vo - - A - eTV t, Vot which proves (*) and completes the

**proof**ofthe lemma. Q.E.D. We shall now state and prove the lemma referred to as CP. For

technical reasons occurring later the following lemma is stated for what might be

...

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### Contents

A Settheoretic Preliminaries | 1 |

Convergence and Uniform Convergence of Generalized | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

27 other sections not shown

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