## 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 complex Consequently contains converges convex Corollary defined DEFINITION denote dense determined differential dimensional disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space identity implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space Math measure space metric space neighborhood norm open set positive measure problem projection Proof properties proved range reflexive representation respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology u-measurable uniform uniformly unique unit valued vector weak weakly compact zero