## Linear Operators: General theory |

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X , the mapping x * +3+ + 2 * , where z * is defined by z * 2 = x * 2 , 3 € 3 . is an isometric isomorphism of X * / 3 + into 3 * . ( b ) If Z is a closed

X , the mapping x * +3+ + 2 * , where z * is defined by z * 2 = x * 2 , 3 € 3 . is an isometric isomorphism of X * / 3 + into 3 * . ( b ) If Z is a closed

**subspace**of a B - space X , the mapping x * * where i * is defined by 7 * ( x + 3 ) ...Page 420

On the other hand , if X is a

On the other hand , if X is a

**subspace**of Y , then each element ye y determines the linear functional f , on X defined by 1 , ( x ) = x ( y ) , 2 € , and the**subspace**I ' = { 1,7 € Y } CX * is obviously total .Page 513

16 If Y is a closed

16 If Y is a closed

**subspace**of a B - space and N is a finite dimensional**subspace**, then Y O N is a closed**subspace**. If y O N is a closed**subspace**, and N is finite dimensional , it does not follow that Y is closed .### 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