## Linear Operators: General theory |

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Page 238

Thus our zero

, we will not ordinarily specify whether the

functions with the stated properties , or of all complex valued functions with ...

Thus our zero

**vector**will be the function which is identically zero . In the list below, we will not ordinarily specify whether the

**spaces**are to consist of all real valuedfunctions with the stated properties , or of all complex valued functions with ...

Page 410

The intersection of an arbitrary family of convex subsets of the

convex . As examples of convex subsets of X , we note the subspaces of X , and

the subsets of X consisting of one point . 3 LEMMA . Let x1 , . . . , Xn be points in ...

The intersection of an arbitrary family of convex subsets of the

**linear space**X isconvex . As examples of convex subsets of X , we note the subspaces of X , and

the subsets of X consisting of one point . 3 LEMMA . Let x1 , . . . , Xn be points in ...

Page 838

7 ( 266 ) remarks concerning , ( 382 ) Atom , in a measure space , IV . 9 . 6 ( 308 )

Automorphisms , in groups , ( 35 ) B - space ( or Banach space ) , basic

properties of , Chap . II definition ... 8 - 12 ( 71 ) remarks on , ( 93 – 94 ) in a

7 ( 266 ) remarks concerning , ( 382 ) Atom , in a measure space , IV . 9 . 6 ( 308 )

Automorphisms , in groups , ( 35 ) B - space ( or Banach space ) , basic

properties of , Chap . II definition ... 8 - 12 ( 71 ) remarks on , ( 93 – 94 ) in a

**linear****space**.### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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### Common terms and phrases

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 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