## Linear Operators: General theory |

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Page 65

14

* with | æ * = 1 and æ * x = læ ] . PROOF . Apply Lemma 12 with Y = 0 . The x *

required in the present

...

14

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

required in the present

**corollary**may then be defined as ( w / times the x * whose...

Page 188

The best known example of Theorem 2 and its

Si , Eis ui ) to be the Borel - Lebesgue measure on the real line for i 1 , n . Then s

P = 1 Si is n - dimensional Euclidean space , and u = My X ... X Min is known as ...

The best known example of Theorem 2 and its

**Corollary**6 is obtained by taking (Si , Eis ui ) to be the Borel - Lebesgue measure on the real line for i 1 , n . Then s

P = 1 Si is n - dimensional Euclidean space , and u = My X ... X Min is known as ...

Page 422

Nelson Dunford, Jacob T. Schwartz, William G. Bade. 11

a linear functional on the linear space X , and let I be a total subspace of X * .

Then the following statements are equivalent : ( i ) f is in l ' ; ( ii ) f is l ' - continuous

...

Nelson Dunford, Jacob T. Schwartz, William G. Bade. 11

**COROLLARY**. Let f bea linear functional on the linear space X , and let I be a total subspace of X * .

Then the following statements are equivalent : ( i ) f is in l ' ; ( ii ) f is l ' - continuous

...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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