## Linear Operators: General theory |

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Results 1-3 of 88

Page 373

This generalizes and abstracts a result

, 1 ] by E. Fischer [ 2 ] . The fact that a linear manifold which is not dense in the

entire space has a non - zero orthogonal complement (

This generalizes and abstracts a result

**proved**for closed linear manifolds in L [ 0, 1 ] by E. Fischer [ 2 ] . 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**...Page 385

18 — 6 . 27 . They are essentially due , at least in the real case , to Stone [ 1 ] ,

although his terminology and proofs often differ from that given here . It should be

mentioned that Theorem 6 . 22 was

18 — 6 . 27 . They are essentially due , at least in the real case , to Stone [ 1 ] ,

although his terminology and proofs often differ from that given here . It should be

mentioned that Theorem 6 . 22 was

**proved**independently by Cech [ 1 ] only ...Page 462

109 ]

Theorem 3 . 9 in which X = Y * and I ' = Y , was

Banach [ 1 ; p . 131 ) and in full generality by Alaoglu ( l ; p . 256 ] . Michael ( 1 )

gave ...

109 ]

**proved**3 . 9 after establishing Lemma 3 . 10 by induction . The case ofTheorem 3 . 9 in which X = Y * and I ' = Y , was

**proved**in the separable case byBanach [ 1 ; p . 131 ) and in full generality by Alaoglu ( l ; p . 256 ] . Michael ( 1 )

gave ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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