## Linear Operators: General theory |

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Page 373

This generalizes and abstracts a result

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 (

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 4.4 ) was ...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 slightly later .Page 463

124 ] also

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 of closure ...

124 ] also

**proved**that in the case of a separable space these notions coincidewith 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 of closure ...

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### Contents

B Topological Preliminaries | 10 |

quences | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

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