## Linear Operators: General theory |

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Page 373

This generalizes and abstracts a result

This generalizes and abstracts a result

**proved**for closed linear manifolds in L2 [ 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 ...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 Čech [ 1 ] only ...Page 463

124 ] also

124 ] also

**proved**that in the case of a separable space hese notions coincide with that of closure in the X topology of X * . Alaoglu ( 1 ; p . 256 ] and Kakutani ( 2 ; p . 170 ) independently established the equivalence of these types ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

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Akad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed closure complex condition Consequently contains continuous functions converges Corollary defined DEFINITION denote dense determined differential disjoint element equation equivalent everywhere Exercise exists extension field finite follows formula function f given Hence Hilbert space implies integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space linear topological space Math means measure space metric space neighborhood norm open set operator problem Proc projection Proof properties proved range reflexive respect Russian satisfies scalar seen semi-group separable sequence set function Show shown statement subset subspace sufficient Suppose Theorem theory topology u-measurable uniform uniformly unique unit sphere valued vector weak weakly compact zero