## Linear Operators, Part 1 |

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Page 289

Nelson Dunford, Jacob T. Schwartz. x * f felg

Theorem 1 , L * is isometrically isomorphic to Lq , so that there is a functional y * e

L * such that æ * * ( * * ) = y * ( 8 ) when g and x * are connected , as in Theorem 1

, by ...

Nelson Dunford, Jacob T. Schwartz. x * f felg

**PROOF**. Let * * < ( L * ) * . ByTheorem 1 , L * is isometrically isomorphic to Lq , so that there is a functional y * e

L * such that æ * * ( * * ) = y * ( 8 ) when g and x * are connected , as in Theorem 1

, by ...

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 434

and proceed as in the first part of the

a subsequence { Ym } of { Xn } such that limm * * * ym exists for each 2 * in the set

H of that

and proceed as in the first part of the

**proof**of the preceding theorem to constructa subsequence { Ym } of { Xn } such that limm * * * ym exists for each 2 * in the set

H of that

**proof**. Let Km = co { ym , Ym + ] , . . . } and let yo be an arbitrary point in ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

12 other sections not shown

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Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

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