## Linear Operators: General theory |

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Page 243

The norm in H is \ x ) = ( x , x ) 1/2 . Remark .

The norm in H is \ x ) = ( x , x ) 1/2 . Remark .

**Hilbert space**has been defined by a set of abstract axioms . It is noteworthy that some of the concrete spaces defined above satisfy these axioms , and hence are special cases ...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

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 without ...Page 838

space of , definition , IV . 2 . ... 6 ( 308 ) Automorphisms , in groups , ( 35 ) B - space ( or Banach space ) , basic properties of , Chap . ... ( See Hamel base ) orthogonal and orthonormal bases in

space of , definition , IV . 2 . ... 6 ( 308 ) Automorphisms , in groups , ( 35 ) B - space ( or Banach space ) , basic properties of , Chap . ... ( See Hamel base ) orthogonal and orthonormal bases in

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

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