## Linear Operators: General theory |

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Page 62

It remains to be

an indirect proof , assume the existence of a vector y , in X but not in Y. Every

vector in the manifold Y , spanned by Y. and y , has a unique representation in

the ...

It remains to be

**shown**that the domain Yo of g is equal to X. For the purposes ofan indirect proof , assume the existence of a vector y , in X but not in Y. Every

vector in the manifold Y , spanned by Y. and y , has a unique representation in

the ...

Page 83

That such results are valid in metric groups was

Banach [ 1 ; Chap . 1 ] and Kuratowski [ 1 ] ) . Conditions of this nature are

extended to polynomial operators by Mazur and Orlicz [ 2 ] . It is sometimes useful

to ...

That such results are valid in metric groups was

**shown**by Banach [ 7 ] ( see alsoBanach [ 1 ; Chap . 1 ] and Kuratowski [ 1 ] ) . Conditions of this nature are

extended to polynomial operators by Mazur and Orlicz [ 2 ] . It is sometimes useful

to ...

Page 553

841 ] has

seen in Theorems 7.4 and 8.12 that in the spaces C and L1 , FCCC W CP .

Grothendieck [ 4 ; p . 153 ) proved that in C , the ideals W and coincide . This is

not the ...

841 ] has

**shown**that in Hilbert space C is a maximal two - sided ideal . We haveseen in Theorems 7.4 and 8.12 that in the spaces C and L1 , FCCC W CP .

Grothendieck [ 4 ; p . 153 ) proved that in C , the ideals W and coincide . This is

not the ...

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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