## Linear Operators: General theory |

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Page 243

It is noteworthy that some of the concrete spaces defined above satisfy these

axioms , and hence are special cases of abstract

instance , the n - dimensional unitary space En is a

product ( x , y ) ...

It is noteworthy that some of the concrete spaces defined above satisfy these

axioms , and hence are special cases of abstract

**Hilbert space**. Thus , forinstance , the n - dimensional unitary space En is a

**Hilbert space**, if the innerproduct ( x , y ) ...

Page 256

Whenever the direct sum of normed linear spaces is used as a normed space ,

the norm will be explicitly mentioned . If , however , each of the spaces X1 , . . . ,

Xn are

explicit ...

Whenever the direct sum of normed linear spaces is used as a normed space ,

the norm will be explicitly mentioned . If , however , each of the spaces X1 , . . . ,

Xn are

**Hilbert spaces**then it will always be understood , sometimes withoutexplicit ...

Page 851

4 ( 59 ) discussion of , ( 82 – 83 ) in F - spaces , II . 1 . ... 72 ( 350 ) , ( 561 ) ideals

of , ( 552 – 553 ) , ( 611 ) identity , ( 37 ) limits of , in B - spaces , II . 3 . ... 17 ( 72 )

remarks on , ( 93 ) Orthogonal elements and manifolds in

4 ( 59 ) discussion of , ( 82 – 83 ) in F - spaces , II . 1 . ... 72 ( 350 ) , ( 561 ) ideals

of , ( 552 – 553 ) , ( 611 ) identity , ( 37 ) limits of , in B - spaces , II . 3 . ... 17 ( 72 )

remarks on , ( 93 ) Orthogonal elements and manifolds in

**Hilbert space**, IV . 4 .### What people are saying - Write a review

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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