## Linear Operators, Part 1 |

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Page 272

The

6.1 ) . Q.E.D. Remark . It should be observed that we can require that the points

S1 , S2 , ... in condition ( 4 ) be contained in a preassigned dense subset of S.

The

**fact**that ( 5 ) implies ( 1 ) is due to Eberlein and is proved in Chapter V ( cf. V.6.1 ) . Q.E.D. Remark . It should be observed that we can require that the points

S1 , S2 , ... in condition ( 4 ) be contained in a preassigned dense subset of S.

Page 373

The

zero orthogonal complement ( proved in 4.4 ) was proved without the assumption

of separability by F. Riesz 87. His proof follows the lines of an argument ...

The

**fact**that a linear manifold which is not dense in the entire space has a non -zero orthogonal complement ( proved in 4.4 ) was proved without the assumption

of separability by F. Riesz 87. His proof follows the lines of an argument ...

Page 386

Nelson Dunford, Jacob T. Schwartz. that S is compact . That this breaks down if C

( S ) is regarded as a topological linear space is demonstrated by the

0 , 1 ] may be mapped in a linear and homeomorphic manner on the space C ...

Nelson Dunford, Jacob T. Schwartz. that S is compact . That this breaks down if C

( S ) is regarded as a topological linear space is demonstrated by the

**fact**that C [0 , 1 ] may be mapped in a linear and homeomorphic manner on the space C ...

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

87 other sections not shown

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