## Linear Operators, Part 1 |

### From inside the book

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Page 188

Q.E.D. As in the case of finite measure spaces we shall call the measure space (

S, 2, u) constructed in

product measure space and write (S, 2, u) = P-1 (S1, 2, u). The best known ...

Q.E.D. As in the case of finite measure spaces we shall call the measure space (

S, 2, u) constructed in

**Corollary**6 from the g-finite measure spaces (S, 2, u,) theproduct measure space and write (S, 2, u) = P-1 (S1, 2, u). The best known ...

Page 246

8

notation of

for w” in *** we have wor” – wor, where r =X; i wo (bo)b,. Q.E.D. From

8

**CoRollary**. A finite dimensional normed linear space is reflerive. - PRoof. In thenotation of

**Corollary**7, n n wor = X boCo)"(b), w” = X bow”(b.), 7–1 f=1 - and thusfor w” in *** we have wor” – wor, where r =X; i wo (bo)b,. Q.E.D. From

**Corollary**...Page 422

... William G. Bade, Robert G. Bartle. 11

the linear space &, and let T be a total subspace of £". Then the following

statements are equivalent: (i) f is in T; (ii) f is T-continuous; (iii) S), - {rf(a) = 0} is T-

closed.

... William G. Bade, Robert G. Bartle. 11

**CoRollary**. Let f be a linear functional onthe linear space &, and let T be a total subspace of £". Then the following

statements are equivalent: (i) f is in T; (ii) f is T-continuous; (iii) S), - {rf(a) = 0} is T-

closed.

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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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