## 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

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

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 slightly later .Page 462

116 ] . Dieudonné [ 3 ; p . 109 ]

induction . The case of Theorem 3.9 in which X = Y * and I Y , was

separable case by Banach [ 1 ; p . 131 ) and in full generality by Alaoglu 1 ; p .

256 ] .

116 ] . Dieudonné [ 3 ; p . 109 ]

**proved**3.9 after establishing Lemma 3.10 byinduction . The case of Theorem 3.9 in which X = Y * and I Y , was

**proved**in theseparable case by Banach [ 1 ; p . 131 ) and in full generality by Alaoglu 1 ; p .

256 ] .

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### Contents

Preliminary Concepts 1 1 Preliminary Concepts | 1 |

B Topological Preliminaries 10 B Topological Preliminaries | 10 |

Metric Spaces | 18 |

Copyright | |

80 other sections not shown

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