## Linear Operators: General theory |

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14

with 12 * 1 = 1 and x * x = \ al . PROOF . Apply Lemma 12 with Y = 0 . The æ *

required in the present

...

14

**COROLLARY**. For every x + 0 in a normed linear space X , there is an æ * X *with 12 * 1 = 1 and x * x = \ al . PROOF . Apply Lemma 12 with Y = 0 . The æ *

required in the present

**corollary**may then be defined as loc1 times the x * whose...

Page 188

The best known example of Theorem 2 and its

Si , Ei , Mi ) to be the Borel - Lebesgue measure on the real line for i = 1 , . . . , n .

Then S = P1 _ 1 Si is n - dimensional Euclidean space , and u = My X . . . XMn is

...

The best known example of Theorem 2 and its

**Corollary**6 is obtained by taking (Si , Ei , Mi ) to be the Borel - Lebesgue measure on the real line for i = 1 , . . . , n .

Then S = P1 _ 1 Si is n - dimensional Euclidean space , and u = My X . . . XMn is

...

Page 246

11 ) of infinite dimensional F - spaces with zero dimensional conjugate spaces .

The following

. 7

11 ) of infinite dimensional F - spaces with zero dimensional conjugate spaces .

The following

**corollary**was established during the first part of the preceding proof. 7

**COROLLARY**. If { b1 , . . . , br } is a Hamel basis for the normed linear space ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

21 other sections not shown

### Other editions - View all

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

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